Ask questions and get helpful responses.

6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b = 1/2with ?1/(1+t) dt with a = 0, b = 1, and repeat the four steps. a. integrate using a graphing utility b.

5,494 results
  1. Calculus

    Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx. A. 45
  2. Calculus

    6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b = 1/2with ?1/(1+t) dt with a = 0, b = 1, and repeat the four steps. a. integrate using a graphing utility b. integrate exactly c. integrate by replacing the integrand with a Taylor
  3. calculus

    use symmetry to evaluate the double integral (1+x^2siny+y^2sinx)dA, R=[-pi,pi]x[-pi,pi]. let g(x) and h(y) be two functions: int(c to d)int(a to b)(g(x,y)+h(x,y))dxdy=int(c to d)int(a to b)g(x,y)dxdy+int(c to d)int(a to b)h(x,y)dxdy
  4. Julia - Green's theorem

    Sorry, I did not see your question ================================= Posted by julia on Monday, December 10, 2007 at 9:15pm. Can someone show me step by step how to work this problem out please. Let C be the triangle with vertices (0,0), (1,0), and (1,2).
  5. Calculus

    Which integral represents the limit as x approaches inf. of 1/n(√(1/n) + √(2/n) + ... √(n/n))? A. int from 0 to 1 of x dx B. int from 0 to 1 of √x dx C. 1/2 * int from 0 to 1 of 1/√x dx D. 2 * int from 1 to 2 of x√x dx
  6. Calc. Help Please.

    Find the value of the definite integral using sums, not antiderivatives: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx Please help... even just showing me how to get started would be greatly appreciated.
  7. Calc,

    Find the value of the definite integral: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx I have no idea how to start this... would I get rid of the fraction?
  8. Calculus

    int(dx/(x^2+9)) u = x/3 Use the indicated substitution (above) to evaluate the integral. Confirm answer by differentiation. Okay, so I found that du/dx is 1/3. dx is 3du. Just by looking at the integral I can tell this is some form of tan^-1(x), if we
  9. Calc.

    Find the value of the definite integral using sums, not antiderivatives: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx Please help.
  10. Computer Science

    (From Lesson 17 of Blue Pelican Java) Use the following code for problems 1 – 15. In each problem state what’s printed. String s = “Lucky hockey puck”; String m = “uck”; int j = 6, z = 99; 1. int k = s.indexOf(m); System.out.println(k); 2. int
  11. Science/Computer Programming

    The purpose of this exercise is to practice reading code and recognizing the traversal patterns in this chapter. The following methods are hard to read, because instead of using meaningful names for each variable and method, they use names of fruits. For
  12. Calculus - Center of Mass

    Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2. X = 1/Area*Integral from a to b: x*f(x)dx Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx How do I find the area for this? Once I know that, is this the correct
  13. Calculus

    For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? You need to let the summation start at n = 3 to avoid the singularity at n = 1 (although you can formally take
  14. Calculus

    This integral does not converge using the normal (Leibniz) definition of integration. Using the identity: int(0-->inf)f(t)/(t)dt = int(0-->inf)F(p)dp, find: integral(0-->inf)(cos(at)+cos(bt))/t dt
  15. AP Calculus

    I need to find the integral: int:(x^2+2x+3)/(x^3+3x+9) dx I think I am supposed to use the rule: int:1/u du=ln|u|+C But I don't know what to do first. Thanks for your help! :-) Oh- and the answer the back of my book gives is (1/3)ln|x^3+3x^2+9x|+C
  16. Java programming

    without running on java, what is the final answer, please show your work. public class sample { public static void main(String[] args){ Sample x = new Sample(); int i = 10; int b = x.g(i); System.out.println(b + i); } public int f(int d){ int n = 0;
  17. Calculus - Integration

    Hello! I really don't think I am understanding my calc hw. Please help me fix my errors. Thank you! 1. integral from 0 to pi/4 of (tanx^2)(secx^4)dx It says u = tan x to substitute So if I use u = tan x, then my du = secx^2 then I have integral of (u^2)
  18. Calculus

    For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x^2)/(sqrt(7x^2+4))dx dx x=?
  19. Calculus

    For the following integral find an appropriate TRIGNOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT((4x^2-3)^1.5) dx x=?
  20. Calculus

    For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. INT((4x^2-3)^1.5) dx x=?
  21. health

    Which of the following is true? A. It would take three to five hours to hydrate the body after a water loss of 3 percent. B. A critical time to replace bodily fluids is while exercising. C. Mild food ingestion during exercise increases water absorption
  22. Calculus

    For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT x(sqrt(8x^2-64x+120))dx x=?
  23. Calculus

    For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x)/(sqrt(-191-8x^2+80x))dx x=?
  24. math

    Find a function f which satisfies the integral equation Int(bounded from 0 to x) t*f(t)dt = Int(bounded from x to 0)(t^2+1)*f(t)dt +x
  25. math

    Find a function f which satisfies the integral equation Int(bounded from 0 to x) t*f(t)dt = Int(bounded from x to 0)(t^2+1)*f(t)dt +x
  26. CALC

    I just need help with changing the order of integration. I can do the actually integral by myself. Thank you :) int f(x,y) dydx where y bounds= 1 to e^x and x bounds= 0 to 4 I thought the new bounds were int f(x,y) dxdy x= 0 to log(y) y= 1 to e^4 Please
  27. calculus please help

    what is the integral of x/(1+x^2)^2 dx This is a question of a past AP exam of calculus BC i know i have to use the substitution method where u=(1+x^2), du=2xdx. I have to find the integral but i'm just focused on the coefficient because i get a different
  28. C++ Programming

    I have to redo programming exercise 5 of chapter 9 using dynamic arrays. but I have the information but I don't know how to use it in a dynamic arrays please help. //Chapter 9: Programming Exercise 5 #include #include #include using namespace std; int
  29. Math

    In the exercise we want to use a substitution to integrate integral xsqrt(x+1)dx. Find the substitution u to transform the integral into integral(u-1)u^(1/2)du. u=?
  30. Calc

    Problems, once again. 1. Compute the average value of: f(x} = x/(x+3) over the interval [-a,a] 2. Find the area of the region bounded by the graph of: y = 2√(x^2 + 1) X axis Y axis Line x = 1 On the first, integrate, then divide the integral by 2a. On
  31. Calculus

    Hello, I'm having trouble with this exercise. Can you help me? Integral of (x* (csc x)^2)dx I'm using the uv - integral v du formula. I tried with u= (csc x)^2 and used some trigonometric formulas, but the expression became too complicated, I couldn't
  32. Calculus

    Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uv-integral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p
  33. Computers

    //program that puts two lists in order in one single list with all the numbers in order import java.util.Scanner; public class listOrder { public static void main (String [] args){ int [] list1; int [] list2; int [] list3; int temp; list1 = new int [10];
  34. Computer Science

    //program that puts two lists in order in one single list with all the numbers in order import java.util.Scanner; public class listOrder { public static void main (String [] args){ int [] list1; int [] list2; int [] list3; int temp; list1 = new int [10];
  35. mathematics

    what does 'dx' signify in the integral and differentiation notation? I was reading integration by substitution method where it is required to replace 'dx' and change the independent variable such that the integral could be transformed.I have read in
  36. java/programming

    Consider the following program segment. Without using Dr.Java, What this program prints? (my class uses Dr.Java) The answer that this program prints which i got was: 22 Is my answer correct? public class sample { public static void main(String[] args){
  37. java/programming repost please help me!

    The ascending order was displaying the same as descending order. how do i get the ascending order to be different from descending order? public static void main(String[] args) { Scanner in = new Scanner(System.in); int n =10; int a[] = new int[n];
  38. Java

    1. Which of the following expression evaluates to a value of 15? 1+2x3+4 (1+2)x(3+4) 1+2x(3+4) (1+2)x3+4** 2. If x is an int which of the following statements adds 5 to the current value of x and store the new value back in x? x=5; x+5; ** x =+ 5; x += 5;
  39. Calculus

    Evaluate the following definite integral: integral at a = -1, b=2 -4dx/(9x^2+30x+25) Would I have to separate them in 3 terms as: -4 ∫1/9x^2 + ∫1/30x + ∫1/25 resulting in: -4/(3x^3)+ (15x^2)+ C? and from there I can replace a and b f(a) - f(b)? Thank
  40. calc

    how do you start this problem: integral of xe^(-2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than 2) You first write
  41. Calculus

    I am trying to find the integral of e^(6x)sin(7x). Apparently, the answer is (6e^(6x)sin(7x) - 7e^(6x)cos(7x))/85) + C and achieving the answer is mostly understandable since it involves integrating the function in parts... that is until I get to this
  42. Calculus

    Evaluate the integral INT(x^4+6x^3+5x^2+8)/(x^2+6x+5)dx Please help.
  43. calculus stewart

    Evaluate the integral Int 7x ln(5x) dx
  44. C++ Algorithms

    Binomial numbers (or binomial coefficients) are important positive integers that arise frequently in computing and mathematics. A function to compute binomial coefficients will have two inputs: n and k. The corresponding coefficient is written as nCk. /*
  45. Computer

    on C++, I want to make an operation like " 2x + y - z ", I wrote something like that but I can' t get the result, where is my mistake? Ty. #include #include int main( void ) { char op; int x; int y; int z; int f; printf ("Enter the operation\n"); scanf
  46. calc

    integral of 1 to e^4 dx/x(1+lnx) 1+lnx = a => dx/x = da dx/ x(1+lnx) = da/a int of da/a = In(a) =>int of dx/ x(1+lnx) = In(1+In(x)) + C from 1 to e^4 for int of dx/ x(1+lnx) = In(1+In(1)) - In(1+In(e^4)) In(1+In(1)) - In(1+In(e^4)) = -In(5) =~ -1.60944 I
  47. Programming

    Consider the following code. public void printNumbers(int x, int y) { if (x < 5) { System.out.println("x: " + x); } if (y > 5) { System.out.println("y: " + y); } int a = (int)(Math.random() * 10); int b= (int)(Math.random() * 10); if (x != y)
  48. Calculus (please help)

    Evaluate the indefinite integral: INT dx/(64+x^2)^2 Please help with this one.
  49. Calculus

    int x^9*(sin(x^5)) Can someone please explain me how to do this integral?
  50. Calculus

    Evaluate the indefinite integral: INT dx/(64+x^2)^2
  51. Calculus

    int x^9*(sin(x^5)) Can someone please explain me how to do this integral?
  52. health

    Which of the following is true? A. It would take three to five hours to hydrate the body after a water loss of 3 percent. B. A critical time to replace bodily fluids is while exercising. C. Mild food ingestion during exercise increases water absorption
  53. computer science

    Algorithm for Binomial Numbers Task Binomial numbers (or binomial coefficients) are important positive integers that arise frequently in computing and mathematics. A function to compute binomial coefficients will have two inputs: n and k. The corresponding
  54. Calculus

    Hello Everyone, I need help with Calc II. 1. Integral from 0 to 1 of (sin(3*pi*t))dt For this one, I got -1/3pi cos (9 pi^2) + 1/3pi 2. indefinite integral of sinxcos(cosx)dx I got sin(cosx) + C 3. Indefinite integral of x over (root (1-x^4))dx I don't
  55. C#

    5) Suppose you have declared an integer array named scores and you make the following method call: TotalScores(scores, num : 1); Of the following overloaded method definitions, which would execute? a. TotalScores(int[] scores) b. TotalScores(int[] scores,
  56. Calculus

    Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^2)dx by subdividing the interval into 8 parts, using (i) the left Riemann sum: INT from 0 to 1 2/(1+x^2)dx (ii) the right Riemann sum: INT from 0 to 1 2/(1+x^2)dx (iii) the trapezoid rule
  57. Calculus

    Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^2)dx by subdividing the interval into 8 parts, using (i) the left Riemann sum: INT from 0 to 1 2/(1+x^2)dx (ii) the right Riemann sum: INT from 0 to 1 2/(1+x^2)dx (iii) the trapezoid rule
  58. Calculus

    Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^2)dx by subdividing the interval into 8 parts, using (i) the left Riemann sum: INT from 0 to 1 2/(1+x^2)dx (ii) the right Riemann sum: INT from 0 to 1 2/(1+x^2)dx (iii) the trapezoid rule
  59. Calculus

    Can someone tell me how to do these? Estimate INT from 0 to 1 2/(1+x^2)dx by subdividing the interval into 8 parts, using (i) the left Riemann sum: INT from 0 to 1 2/(1+x^2)dx (ii) the right Riemann sum: INT from 0 to 1 2/(1+x^2)dx (iii) the trapezoid rule
  60. math quadratic equations

    a) expand and simplify: (4x-3)(x+1) i get 4x^2+x-3 ? b) factorise: 2x^2 + 13x + 15 c) find y-int, x-int and vertex of: y= x^2-3x-4 i get y-int = -4, but loose it from there :(
  61. computer science

    IHow do you refractor this: public class Employee { private boolean isPartTime; private int seniority; private int monthsDisabled; public Employee(boolean isPartTime, int seniority, int monthsDisabled) { this.isPartTime = isPartTime; this.seniority =
  62. Calculus AP

    areas between the curves x=y^2-2, x=y, y=3. int[a,b](f(y)-g(y)) dy i know how to graph. but im have problem with integral.
  63. Calculus

    Evaluate the indefinite integral of InT(-x^3+9x^2-3x+2)/(x^4-2x^3) I got ((1-2x)/(2x^2))+3*ln(2-x)-4*ln(x) but apparently that's not the answer...
  64. Calc

    f(x,y,z) = y; W is the region bounded by the plane x+y+z=2;cylinder x^2+z^2=1. and y=0. What I have set up isL 4 int(0 to 1) int(0 to sqrt(1-x^2)) int(0 to 1-x-y) y dydzdx. But solving this is pretty cumbersome. Any other ideas?
  65. calc asap!

    can you help me get started on this integral by parts? 4 S sqrt(t) ln(t) dt 1 please help! thanks! Integral t^(1/2)Ln(t)dt = 2/3 t^(3/2)Ln(t)- 2/3 Integral t^(1/2) dt = 2/3 t^(3/2)Ln(t) - 4/9 t^(3/2) Simpler method: Integral t^(a)dt = t^(a+1)/(a+1)
  66. Calculus

    Evaluate the indefinite integral of InT(-x^3+9x^2-3x+2)/(x^4-2x^3) I got ((1-2x)/(2x^2))+3*ln(2-x)-4*ln(x)+c but apparently that's not the answer... and I don't know why.
  67. Calculus

    Evaluate the indefinite integral of InT(-x^3+9x^2-3x+2)/(x^4-2x^3) I got ((1-2x)/(2x^2))+3*ln(2-x)-4*ln(x)+c but apparently that's not the answer... and I don't know why.
  68. math

    int( absolute(x-1) + sqrt(9-x) ) Hint: you may interpret the integral as an area.
  69. Calculus II/III

    A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of our question , the surface
  70. computer science

    int *reverse(const int *, int); int *temp; temp = reverse(arr1,N); int *reverse(const int *arr1, int N) { int *arr2; arr2 = new int[N]; for(int count = 0; count < N; count++) { for(int index = (N-1); index
  71. Calculus

    Integrate x dx/(1-x). I have proceeded thus- Int xdx/(1-x)=int -(x-1+1)/(x-1) =-Int[1+ 1/(x-1)]dx =-Int dx-Int dx/(x-1) =-x-log(x-1). On differentiating, we get original expression- d/dx[-x-log(x-1)]=-1-1/(x-1)=-x/(x-1)=x/(1-x). However, the answer in the
  72. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a to b of g of x dx ~the
  73. check my precalc

    #1. (3x^3-4x^2-3x+4)/(x^3-5x) my answers: y-int: NONE x-int: 1, -1, and 4/3 x asymtope: x= 0 and +- square root of 5 y asym: y=3 If it crosses horiz asym: idk i need help on this #2. (x^4-7x^2+12)/(x^2-5x+4) x-int: -2, 2, and +- square root of 3 y-int: 3
  74. Precalc

    #1. (3x^3-4x^2-3x+4)/(x^3-5x) my answers: y-int: NONE x-int: 1, -1, and 4/3 x asymtope: x= 0 and +- square root of 5 y asym: y=3 If it crosses horiz asym: idk i need help on this #2. (x^4-7x^2+12)/(x^2-5x+4) x-int: -2, 2, and +- square root of 3 y-int: 3
  75. PHYSICS HELP PLEASE!

    The maximum wavelength of light emitted from a blackbody that will emit electrons from a given piece of metal is 255nm. What is the fraction of total energy emitted from the black body that emits electrons? I set up the integral:
  76. Calculus

    Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral
  77. Calculus

    Evaluate the integral by interpreting it in terms of areas as 0 goes to 12 |2x - 7|dx? This is my work so far: 2x-7=0 x=7/2 slope = 2; y-int = (0, -7) Area of a triangle is 1/2BH.
  78. English

    1. I am into sports. (What is the meaning of this sentence?) 2. Exercise is good for the health. 2-1. Exercise is good for health. 2-2. Exercise is good for your health. 2-3. Exercise does good for people. (Are all correct?) 3. Our athletic meet took place
  79. computer

    If int main() { int a=1; int *p; how do the following statements differ 1) p=&a; 2) *p=&a; 3) p=a; 4) printf("%d",p); 5) printf("%d",*p); and what does int **a mean
  80. java/programming Please Help Me!!

    this java program is giving me errors. can someone please help me public static void main(String[] args) { int[] num = new int[10]; gatherInput (num); divide(num); } private static void gatherInput(int[] num) { Scanner in = new Scanner(System.in);
  81. Advanced Functions

    Given the following transformations 𝑦 = 3𝑓(−2𝑥 + 8) − 6 to the parent function 𝑓(𝑥) = 𝑙𝑜𝑔2(𝑥), describe (in words) how to determine the following key features of the transformed function without graphing: Domain: Range:
  82. Java programming

    how do i add prime numbers in this java code: public class PrimeNumbers { public static void main(String[] args) { int[] array = new int[10]; Scanner in = new Scanner(System.in); System.out.println("Enter the elements of the array: "); for (int i = 0; i <
  83. Mathematics-Integration

    Question: For any positive integer n,show that integrate.[(sin x)^2n dx ] from o - π/2 = [(2n)!*π]/[(2)^(2n+1)*(n!)^2 ] What I thought: Let I =int.[(sinx)^2n dx] And again I= int.[ (sin(π/2-x))^2n dx] = int.[ (cos)^2n dx] 2I= int.[(sin x)^2n + (cos
  84. Calculus

    I have done Int(1/ax)dx=1/a*Int(1/x)dx =[(log x)/a] + C. The working in the book is Int(1/ax)dx=1/a*Int(a/ax)dx =[(log ax)/a]+C. Which one is correct and where is the error in my working, if so?
  85. Calculus

    Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t - e^-t)^2 +
  86. AP Calculus BC

    How would i go about using partial fraction decomposition on the integral, (int) (x+2)/(x^2+4x+5) dx. Is there a way to do this utilizing complex number decomposition?
  87. AP Calculus BC

    How would i go about using partial fraction decomposition on the integral, (int) (x+2)/(x^2+4x+5) dx. Is there a way to do this utilizing complex number decomposition.
  88. Math

    lim as b approaches infinity of integral of xe^-x^2 from 0 to b aka lim b->inf int(0,b) x*e^(-x^2) dx
  89. Mathematics -Integration : to Steve

    But how do we integrate ln|1+tanx| da X=theta =int.[ln|cos x|dx] +int.[sin x| dx ] - int.[ln|cos x| dx] ?
  90. Calc 121

    How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x)) There is a trick to this one that grealy simplifies the integral. Let u = x^3 + 2x. Then du = (3x^2 + 2)dx The integral then bemoces just the integral of du/u,
  91. c++ program

    how can a modfiy this source code to a menu. #include #include #include main() { char cYesNo = '\0'; int iResp1 = 0; int iResp2 = 0; int iResp3 = 0; int iElaspedTime = 0; int iCurrentTime = 0; int iRandomNum = 0; int i1 = 0; int i2 = 0; int i3 = 0; int
  92. math

    write the slop - intercept form of the equation wiht the given slope and intercept slope:2/5 x-int=4.5 i knwo how to do it with y-int but how doyou do it with x- int?
  93. Java Programming

    Hey! Thanks for checking my question out! ____ 10. If x is a sorted array of int values, which of the following shows a call to a method of the Arrays class that will determine if the value 7 exists in the array? (1 point) a) int loc =
  94. Calculus

    Int tanx sec^2x dx can be taken as (by putting it in form of Int xdx) Int secx.secx tanx dx=(sec^2x)/2 Int tanx.sec^2x dx=(tan^2)/2. Which one is correct and why is the difference?
  95. Calculus

    Integral of dx/{(x+1)sqrt(x^2+4x+2)} is given as -arcsinh{(x+2)/(xsqrt3)}, but I am not getting it.? The hint given is 'Put 1/(x+1)=t' Using it, the expression reduces to Int. -1/sqrt(1+2t-t^2). How to proceed further to get the desired result?
  96. programming

    m trying to create an arraylist that's sorted but I have no idea how to sort the numbers. I cant use the array.sort method here is my code: public class Testing { private int [] data; private int count; private static int defCapacity = 10; public Testing
  97. computer science

    Im trying to create an arraylist that's sorted but I have no idea how to sort the numbers. I cant use the array.sort method here is my code: public class Testing { private int [] data; private int count; private static int defCapacity = 10; public Testing
  98. Computer Science

    public class RandomPhoneNumber { public static void main(String[] args) { int num1=(int)(Math.random()*7); int num2=(int)(Math.random()*7); int num3=(int)(Math.random()*7); int set1=(int)(100+Math.random()*642); int set2=(int)(1000+Math.random()*8000);
  99. English

    Fill each blank with a coordinating word or phrase and proper punctuation in order to form a combined sentence. 1.Exercise has become very popular today _______ millions of Americans run or jog. 2.Exercise is fun _______ exercise is a good way to stay
  100. Calc Jacobian

    Thanks "I know that the xy region is the line x=y y=0 and y=1- x/2)" It is helpful to rewrite the region in the x-y plane by specifying the three lines and the endpoints, i.e. the points where they intersect. If you insert these points in the formula for U

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