# Calculus - Integrals

17,052 results

### calculus

[integrals]2/tsqrt(t^4+25) integrals of two over t square root of t to the 4th plus 25

### Calculus

Write 2.445353535353... as a fraction I'm learning integrals right now and this is part of the exercises under it. Is there a trick to this? Using integrals? Thank you very much!

### Calculus indefinite integrals

Evaluate the following indefinite integrals using substitution a) ∫ xsqrt(x^2-7) dx b) ∫ x^(2/3)(1/5x^(5/3)+2)^4 dx

### Calculus (Definite Integrals)

How many definite integrals would be required to represent the area of the region enclosed by the curves y=(cos^2(x))(sin(x)) and y=0.03x^2, assuming you could not use the absolute value function? a.) 1 b.) 2 c.) 3 d.) 4 e.) 5

### calculus

There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals converge. First of all...

### calculus

There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals converge. First of all...

### Calculus AB

Consider the region bounded by the graphs of the equations x=y^2 and y=3x. Set up 2 integrals, one with respect to x and the other with respect to y, both of which compute the volume of the solid obtained by rotating this region about the x-axis and evaluate the integrals.

### Calculus - evaluating integrals

I'm really having trouble with this current topic that we're learning. Any explanations are greatly appreciated. Evaluate the integrals: 1.) ∫ (2-2cos^2x) dx 2.) ∫ cot3x dx 3.) ∫ ((e^(sqrt x) / (sqrt x) dx))

### MATH 2B Calculus

Consider the area between the graphs x+4y=14 and x+7=y^2. This area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals They ask to use two integrals so i put f(x) from -7 to 2 which is correct but for g(x) i put 2 ...

### Calculus Please Help4

Consider the area between the graphs x+2y=9 and x+6=y^2. This area can be computed in two different ways using integrals First of all it can be computed as a sum of two integrals as integral f(x)dx from a,b + integral g(x)dx from b,c I got a=-6 b=3 c=19 but what does f(x)=? g(...

### Calculus Area between curves

Consider the area between the graphs x+6y=8 and x+8=y2. This area can be computed in two different ways using integrals First of all it can be computed as a sum of two integrals where a= , b=, c= and f(x)= g(x)= I found a, but not b or c. I can't seem to figure out f(x) and g(...

### MATH

Evaluate by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.

### Calculus integrals

(e^(3x)-2e^(2x)+(5e^x))/(e^x+1) how do I do this what is the techniques??

### Calculus

Integrals: When we solve for area under a curve, we must consider when the curve is under the axis. We would have to split the integral using the zeros that intersect with the axis. Would this be for all integrals? What if we just want to "find the integral", without finding ...

### Calculus - Integrals

What is the integral of arctan x?

### Calculus

[Integrals] h(x)= -4 to sin(x) (cos(t^5)+t)dt h'(x)=?

### Integrals calculus

7/x^2-8 does it give you 7ln(x^2-8)

### calculus 2

integrate x^5/(x^2 + sqrt(2)) using a table of integrals

### Calculus

11) Find the following indefinite integrals. ∫x/(x+9)^(1/2)dx

### calculus

evaluate the definite integrals 1 ∫ root(1+3x) dx 0

### Calculus - Definite Integrals Please Help!

h(x)=∫[-3,sin(x)] (cos(t^3)+t) dt

### Calculus - Integrals

Integral of (dt/[sqrt(t)+25tsqrt(t)]} From 1/75 to 3/25 I'm at a complete loss at what to do.

### Calculus

definite Integrals (using fundamental Theorem) Evaluate from -1 to 2(x^2 - 4x)dx

### Calculus (integrals)

Find the integral:8x^7+6/(x^8+6x)^2 I got ln(x^8+6x)^2 but apparently that is wrong.

### calculus

Use table of integrals to evaluate the integral of x^4 sinxdx.

### Calculus

Hi. How can I integrate 1/(X^3 +1) ? Thank you to anyone who can help me :-) Write 1/(x^3 +1) as 1/[(x+1)(x^2-x+1)] Then use integration by parts, letting dv = dx/(x^2 -x +1) u = 1/(x+1) du = log (x+1) v = (2/sqrt3)arctan[(2x-1)/sqrt3] That should take you to the answer. I ...

### Calc or Pre calc

I am having trouble doing this problem. I know how to do indefinate integrals, but I don't know how to do definate integrals. Can you show me how to do this. Evaluate 5 (x^3-2x)dx 2

### Maths

What is the answer for these questions:- 1) Indefinite Integrals gcx) = (8 + 39x ^ 3) / x 2) Indefinite Integrals hcu) = sin ^2 (1/8 u) 3) Evaluate x ( 8 - 5 x ^2) dx Thank you

### calculus

Use integrals to prove that the volume of a sphere of radius R is equal to (4/3)(pi)R^3

### calculus

Use the Table of Integrals to evaluate the integral (x sine(6x^2)cos(7x^2)dx)

### Calculus

Find the values of c guaranteed by the mean value theorem for integrals. f(x)= x^3 [0,3]

### Calculus - Integrals

Consider the region enclosed by the graphs of x=y^2-5 and x=3-y^2 a)Express the area of this region by setting up an integral with respect to x b) Express the area of this region by setting up an integral with respect to y c) Find the area of this region by evaluating one of ...

### math, calculus 2

Consider the area between the graphs x+y=16 and x+4= (y^2). This area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals integrate from a to b of f(x)dx + integrate from b to c of g(x)dx What is the value of a, b, c...

### Calculus

What is the connection between improper integrals, Riemann sums, and the integral test?

### Calculus

Graph the integrands and use areas to evaluate integrals (integrate(3&-3)) root(9-x^2) dx

### Calculus integrals

Find the value of the right-endpoint Riemann sum in terms of n f(x)=x^2 [0,2]

### Calculus integrals

Suppose f(x)=∫ (from 0 to x) (t^2-36)/2+cos^2(t) dt. For what value(s) of x does f(x) have a local maximum?

### Math (Calculus) Integrals

Evaluate the integral using the following values. 8 ∫ x^3 dx = 1020 2 8 ∫ x dx = 30 2 8 ∫ dx = 6 2 2 ∫ x^3 dx = ? 2

### single variable calculus - indefinite integrals

integral of (1-(sinx)^2))/(cosx)dx i don't know what to make my "u" for u-substitution

### calculus

Evaluate the following integrals by using appropriate method : ∫cos ^3 ( 2x-5 )dx help

### Calculus

Find all values of c that satisfy the Mean Value Theorem for integrals for f(x)= x^{2} on the interval [-3, 3]

### Calculus - Integrals

The region bounded by y=x^2, x=y^2 is rotated about the line y=-3. The volume of the resulting solid is:

### College Calculus

Could someone explain how to distinguish improper integrals in non-mathematical terms so I may understand? Thanks!

### Calculus

Describe the solid whose volume is represented by the following definite integrals. The integral of 2pi(x-1)e^x from 2 to 7.

### calculus showed work

find the area of the rgion bounded by the graphs of y=x^3-2x and g(x)=-x i drew the graph and half of the graph is above the xaxis and the other half is below the axis. so the integrals i came up with are two because i broke them up and i combined the answers at the end: ...

### calculus

evaluate the following indefinite integrals by substitution & check the result by differentiation. ∫(sin2x)^2 cos2xdx

### Math (Integrals) (Basic Integration)

I am given two integrals a and b a) ∫ 1/(1 + x^4) dx b) ∫ x/(1 + x^4) dx The main difference between the two integrals appears to be the "1" and "x" on the numerators. While they both resembles closely to the basic integration of arctan: ∫ du/(a^2 + u^2) = 1/a * arctan(u...

### AP Calculus

how do you evaluate integral of [lxl] from (0,2) , a step function. would you just do it as if it were a absolute value and then do two different integrals?

### calculus 4

a solid cube, 2 units on a side, is bounded by the planes x=+-1, z=+-1, y=3 and y=5. Find the center of mass using triple integrals.

### calculus II university

prove the following integrals: a)sin3xcos7xdx = -1/20cos(10x)+1/8cos(4x) b)sin8xcos3xdx = -1/22cos(11x)-1/10cos(5x)

### Calculus

"Evaluate the following indefinite integrals: "S" (3x^2 -2)/(x^3 - 2x + 1)^3 dx" We're practicing the substitution rule, and I know how to do it, but I don't know what/how to substitute in this question. btw: "S" is the integral sign.

### Calculus

Integrate [1/square root of(e^(2x)-1)]. I have to use u substitution. We are doing the integrals of inverse trig functions, but I cannot get it to work out!

### Calculus - Integrals

Find the volume of the solid of revolution obtained by revolving region bounded by the parabolas 2y=x^2 and y^2=4x about the x-axis

### Calculus

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = ex, x = 1, and y = 1 is revolved around the line y = -2

### Calculus

Find the area of a function using integrals that equals .5 (can range from .499 to .504) There has to be three regions for the equations

### calculus1

Set up the integrals that can be used to find the area of the region by integrating with respect to X and Y (the region is bounded by y=3x,y=x,y=4-x) Anyone help me set up the integrals??

### Calculus

Consider the area between the graphs x+1y=12 and x+8=y2 . This area can be computed in two different ways using integrals First of all it can be computed as a sum of two integrals Interval a to b f(x)= i put 12-x but it's wrong Interval c to b f(x)= i put (x-8)^(1/2) but it's ...

### calculus

set up sums of integrals that can be used to find the area of the region bounded by the graphs of the equations by integrating with respect to y y=square root of x; y= -x, x=1, x=4

### statistics

Suppose that fÈ and fX|È are described by simple closed-form formulas. Suppose that È is one-dimensional but X is high-dimensional. a) Suppose that a specific value x of the random variable X has been observed. Is it true that the calculation of the LMS estimate will always...

### calculus

evaluate the following integrals by any means possible: b. integral from -1 to 1 (w/ (w^2+1)) (dw) c. integral from -3 to 0 sqrt(9-x^2)dx

### Calculus

ç1 0 x^2dx=1/3. Use this and the properties of integrals to evaluate ç1 0 10−2x^2dx

### Calculus

1. Evaluate the following integrals (a) 4x2 +6x−12 / x3 − 4x dx

### Calculus

Evaluate the following integrals. Show all the steps in your calculation. a. ç_0^2(3x^3 - x^2 + 2)dx b. ç_0^1(e^2x - x^2)dx c. ç1/(x+3)dx

### Calculus

Find the biggest value of c that satisfy the Mean Value Theorem for integrals for f(x)= 1/(x+1)^6 on the interval [0,7]

### Calculus

I need help with integrals and I need help with the problem. Integral of 4/sqrt(x)dx

### Calculus

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 4√x [4, 9]

### calculus

Evaluate the following integrals using the given substitutions. (a) (3x^2 + 10x)dx/(x^3 + 5x^2 + 18 , substitution u = x3 + 5x2 + 18; (b)(14x + 4)cos(7x^2 + 4x)dx,substitution u = 7x^2 + 4x.

### Calculus (math)

Consider the area between the graphs x+3y=35 and x+5=y2. This area can be computed in two different ways using integrals

### Calculus (improper integrals)

the integral from 0 to lnx of lnx/(x^1/2) thanks!

### calculus

It is known that if m <= f(x) <= M for a <= x <= b, then the following property of integrals is true. m(b-a) <= int_a^b f(x)dx <= M(b-a) Use this property to estimate the value of the given integral. ? <= int_0^3 3/(1+x^2)dx 2 <= ? solve for the ?

### Calculus (Integrals)

Evaluate the following expression: d/dx (integration sign: upper=1 and lower= -3) (2t^3 + 3)dt = I am given the following options: 2t^3 + 3 56 5 -28.0 None of the above

### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 5 - x^2 on the interval 0 to sqrt 5 . If so, find the x-coordinates of the point(s) guaranteed by the theorem.

### Calculus (Definite Integrals - Arclength)

Using the trapezoid rule with n = 8 to approximate the arc length of the graph of y = 2x^3 - 2x + 1 from A(0,1) to B(2,13) you get (to three decimal places): A.) 6.900 B.) 13.896 C.) 14.093 D.) 13.688 E.) 13.697

### calculus

prove the following integrals: a)sin3xcos7xdx = -1/20cos(10x)+1/8cos(4x) i know i have asked this question before but i am very confused bobpursley, can you please show me the steps of proves. thanks in advanced

### Calculus

Hello, Tutors! I am struggling on how to do problems related to finding the volume using integrals. Could you please help me? Any easy-to understand resources? Thank You for all your help. I am thankful for you tutors!!!!!!!

### calculus

For large values of n, the Riemann sum 1/n(sin0 + (pi/2n) + sin(2pi/2n) +sin(3pi/2n)+...sin((n-1)pi/2n)) is an approximation for which of the following integrals?

### Cal

consider the area between the graphs x+3y=1 and x+9=y^2. this area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals where a=,b=,c= and f(x0= and g(x)=. Alterntaively this area can be computed as a single integral

### Cal

consider the area between the graphs x+3y=1 and x+9=y^2. this area can be computed in two different ways using integrals. First of all it can be computed as a sum of two integrals where a=,b=,c= and f(x0= and g(x)=. Alterntaively this area can be computed as a single integral

### Calculus - Integrals

I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S-1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.

### Calculus - Integrals

I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S-1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.

### CALCULUS 2!!! PLEASE HELP!!

I'm having trouble with this question on arc length: y=lnx, (squareroot)3/3 greater than or equal to x less than or equal to 1 It sounds as if you want the length of the y = ln x curve from x = sqrt(3)/3 (0.57735..) to 1. The formula for the arc length of a line y(x) is Length...

### Calculus (integrals)

Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to solve this, can you help ...

### Calculus

How do I solve this problem without integrals or derivatives? Find the distance traveled in 14 seconds by an object that is moving with a velocity of v(t) = 11 + 6cos t feet per second. A. 154.8204 B. 156.1704 C. 159.9436

### Calculus

integral of cscx^(2/3)(cot^3)x i know that cot^2x is csc^2(x)-1, but i just don't understand how to solve the cscx^(2/3), any help? i also know that its trig integrals/substitution...

### Calculus

I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5-(u^2))du I have a feeling I will be able to find the derivative easily, I'm just having trouble...

### Calculus

which of the following integrals results from making the substitution u=x^3 in orer to find (squiggly vertical line)x^2cos(x^3)dx ~cos u du ~u^2 cos u du ~u^(2/3) cos u du1/3 os u du ~3 cos u du

### calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 − 9x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem

### calculus

Calculate Integrals: x= 2 cos â - cos 2 â -1, y= 2 sin â - sin 2 â? I need the procedure. The answer is: 6ð Thank you!

### Calculus (Integrals and Derivatives)

Evaluate the following expression: d/dx (integration sign: upper=1 and lower= -3) (2t^3 + 3)dt = I am given the following options: 2t^3 + 3 56 5 -28.0 None of the above Would the result of the expression be 0 or 5???

### Calculus

Evaluate the following integrals {e˄x+e˄-x/ e˄x dx

### ap calculus

Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1? All the answers are preceded by the integral sign from 0 to 1. (a) sqrt[1 + e^(2*(x+e^x))] dx (b) sqrt[1 + e^(4x)] dx (c) sqrt[1 + e^(x+e^x)] dx (d) sqrt[1 + e^(2e^x)] dx (e) sqrt[e...

### Calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 - 9x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. I think one point is zero.

### Calculus

Can someone help me to evaluate these two integrals? INT dx/(x^2*sqrt(x^2-25)) and INT (from 0 to 1) -5*sqrt(x^2+1) dx

### calculus

how do you calculate the instantaneous rate of change. is that the derivative. also: if f is the antiderivate of (x^2)/(1+x^5 such that f(1)=o then f(4)=? How would i find the integral of that? i don't even know what the first step is to get the answer. also, on this question...

### vector calculus

Show that the given line integral is independent of path.Then, evaluate the line integral I by finding a potential function f and applying the Fundamental Theorem of Line Integrals. I=ç_{(0,0)}^{(1,2)}(x+y)dx+(x-y)dy

### calculus help work

a force of 1250 pounds compresses a spring 5 inches from its natural length. find the work done in compressing the spring 8 additional inches. f=kd 1250=k5 k=250 then what do i do. i have to do this the calculus way, not the physics way. by using integrals the answer choices ...

### [Calculus] U-substitution for Integrals

Integrate from 1 to 5 of (3x-5)^5 dx = Integrate from a to b of f(u) du where (I have solved this part) u = 3x-5 du = 3 a = 0 b = 12 The original value of the integral is 165888 via calculator here's my last question, and it has to be in terms of u: f(u) = ? (Again, in terms ...

### calculus

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x^3 − 9x on the interval [−1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. Not quite sure how to do this one at all to be completely honest. ...

### Calculus

integral 1 to 500 (13^x - 11^x) + integral 2 to 500 (11^x - 13^x) dx = (answer: 14.946) I tried typing the integrals in the graphing calculator to get the answer, but it says overflow. Any help on solving this? Thanks!