How do you integrate [(x^2)(cos(2(x^3)))]?

5,185 results

Mathematics-Integration

Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate f(a-x) dx from (0-a) From that and by sin(2x)=...

Integral calculus

Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals is using partial integration. So, look ...

Calc 1

integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3 integrate form pi^2/36 to pi^2/4 (cos(x^1/2))/(xsin(x^1/2))^1/2 integrate from 0 to pi/3 (tanx)/(2secx)^1/2

calculus

1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (5xCos3x) dx I Will be happy to critique your thinking on these. 1) Derive a recursive relation. 2) Simplest by replacing sin(bx) by Exp[i b x] and taking imaginary part at the end. 3) First integrate sin(yx) ...

Calculus

How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

PLZ integrate

integrate cos^3x dx tnk U

Integral calculus

Please do help solve the followings 1) Integrate e^4 dx 2) Integrate dx/sqrt(90^2-4x^2) 3) Integrate (e^x+x)^2(e^x+1) dx 4) Integrate xe^x2 dx e^4 is a constant. 3) let u= e^x + x du= (e^x + 1)dx 4) let u= x du=dx v= e^x dv= e^x dx

math

integrate sqrt(2((sin(x))^2 + 50((cos(x))^2 - 10sin(x)cos(x))

Math

integrate (sin^8 x - cos^8 x)/(1 - 2sin^2 x * cos^2 x) w.r.t. x

Trig Identities

Why does cos^2(x)= 1/2cos(2x)+1/2? I am trying to integrate, but the answer key says to first rewrite the expression like the above. I don't get how to change cos^2(x) into that. Explain?

Maths

keep getting stuck for integrate e^(bx) cos x i get = cos x e^bx/b - int -sin x e^bx/b = cos x e^bx/b - -sin x e^bx/b^2 - int - cos x e^bx/b^2 this is where i get stuck please help

math

the question asks to integrate cos(t)/ (5sin(t)+8)^2 the answer i got was xcos(t)/(5sin(t)+8)^2 this is not right i believe there is something wrong with the x in front of the cos.... please heplp

integrate

integrate du/3u and integrate x/x^2 dx it might be simple...i just need a head start...tnx

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] ?

math

integrate Cos^7(2x)

Calculus

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help.

college math

how do you integrate (cos^2 x)^4

Math

Integrate (sin^2(t)+1)/(cos^4(t))dt

Calculus

Integrate [sinx/(1+cos^2(x))] from pi/2 to pi.

maths

integrate -sinx/ã4+cos^2x dx

Integration need help

Integrate (6x^2-cos(2x))dx??

Calculus

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at 12:45am 1/2 ∫ 1/(sin(x/2)cos(x/2))dx let u...

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 series and integrate term ...

Math

Find the greatest value of a,so that integrate [x*root{(a^2-x^2)/(a^2+x^2)} ] from 0-a<=(π-2) Let I =integrate{ [x*root{(a^2 - x^2)/(a^2+x^2)}]dx } from 0-a I used the substitution u=root[x^2+a^] to simplify the further. After substituting and changing limits I got, I=...

Math

Integrate: ∫(cos^3⁡ x)^2 dx

Calculus

How do we integrate [(cosx)^2(nx)(sin(nx))]/[a-(cos(nx))] dx?

calculus 2

Justify, with a written explanation or a mathematical reasoning and with a sketch of at least two different cases, the following properties of integrals: a) If f(x) is less than or equal to g(x) for a<=x<=b then integrate from a to b of f(x)dx is less than or equal to ...

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 x)^2n dx] 2I= int.[ (sin ...

Calculas

Integrate: Cos^7(2x) Explanation would be helpful

Calculus

Integrate Cos^7(2x) Explanation would be helpful

Calculus - MathMate Please help

ok, i tried to do what you told me but i cant solve it for c because they cancel each others out! the integral for the first one i got is [sin(c)cos(x)-cos(c)sin(x)+sin(x)+c] and the integral for the 2nd one i got is [-sin(c)cos(x)+cos(c)sin(x)-sin(x)+c] I don't know what to ...

calculus

integrate it by integrating factor (cos^3x)dy/dx +ycosx=sinx

Calc.

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

calculus

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

math

Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b? or is it something different. When plugging it in the calculator, do we enter it with cos and then the (cos^-1(19 pi)).

Calculus

Can someone help me to integrate by substitution the indefinite integral: (sinx)/ (1+cos(^2)x)?

calculus

We are not going to do that work for you, but will be glad to help you. The unit sphere is the sphere with radius 1 centered in the origin. They give you the coordinates of a vector. Compute the dot product of the vector and the local surface area normal and integrate it over ...

Math

integrate dy/dx=x(y^(1/2))(cos^2(y^(1/2))^2) I know I need to separate, and Iv'e moved dx to the right side with dy on the left. Don't know how to go on.

pre-cal

Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48 cos^4 x + 18 cos^2 x - 1 I assume you are ...

Math

Solve it showing detail steps..please. Integrate : ∫(cos^3 x)^2 ⁡dx

Math Integration

i keep getting stuck and i think im missing something integrate by parts e^(bx) cos x dx thanks

Adv Calculus

Integrate the following indefinite integral: (sin7x)^12 * (cos7x)^3 Hint: sin^2 + cos^2 = 1

Math

Please help me the way through this sum Integrate Cos squared(3x) btwn x=pie/2 andx=0

calculus help

integrate cos^10xdx.. .plz show working i really wanna learn these thanks anyway

maths

Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]

maths

Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]

Calc

How do you solve ∫sin(3x+4)dx? I got the -cos(3x+4) part, but do you have to integrate the 3x+4 too? Does chain rule apply?

Calculus

Use the trapezoidal rule with n = 5 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) from x=1 to 5

Calculus

Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) x=1 to 5

Math - Solving Trig Equations

What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x)) = 4cos^4(x) - 4cos^2(x) + 1 5cos^4(x) - 5cos^...

calculus very hard help

integrate:cos^10xdx even with the previous hint a tutor here gave me i still don,t know it

TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...

Fourier Sine Series Q

I have the function f(x) = cos(x) on the interval from 0 to pi and I need to comput the Fourier sine series. I have the integral of cos(x) multiplied by sin(nx), I can't figure out a way to integrate them! The "n" gets in the way, what do I do?

calc

find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the anti-derivative you plug in -3 to the anti-derivative and ...

Mathematics - Trigonometric Identities

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y)(sin^2y) / (sin^...

calculus help please

dy/dx = 2y^2 Integrating...y=2/3 y^3 + C put 1,-1 into the equation, and solve for C. Then find the y for x=2 if y= a^uhttp://math2.org/math/integrals/tableof.htm see exponential functions. dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=? how do i get x in the equation. do ...

trig

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity = sin(145-75) = sin 70 = cos 20 note that...

Precalculus

Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these two, it would be great help.. Thankyou ...

math

Find the exact value of cos 300 degrees. thanks guys cos 300 = 1/2 = 0.500 how do you know? I am supposed to show my work. You ought to know the rule on 30-60-90 triangles. If the hyp is 2, the shorter side is 1, and the longer side is sqrt3. what does that have to do with ...

Trigonometry

Write equivalent equations in the form of inverse functions for a.)x=y+cos è b.)cosy=x^2 (can you show how you would solve) a.) x= y+ cos è cos è = x-y theta = cos^-1(x-y) b.) cosy=x^2 cos(y) = x^2 y = Cos^-1(x^2)

tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) Add the two equations: sin(a+b) + sin(a-b) = ...

Math Integration

Integrate: f (x)/(2x + 1) dx let f represent integrate sign let u = x, du = dx => dx = du = f (u)/(2u + 1) du = f u (2u + 1)^(-1) du = (1/2)u^2 (ln|2u + 1|) + c = (1/2)x^2 (ln|2x + 1|) + c ...what did I do wrong? The correct answer is (1/2)x - (1/4)ln|2x + 1| + c

Calculus AB

Please help me integrate this equation using partial fractions: Integrate [(x^2+5)/(x^3-x^2+x+3)]dx. Thank you very much.

trig

Show that 1-cos2A/Cos^2*A = tan^2*A 1-cos2A/Cos^2*A = [Cos^2(A) - Cos(2A)]/Cos^2(A). Substitute: Cos(2A) = 2Cos^2(A) - 1: [1 - Cos^2(A)]/Cos^2(A)= Sin^2(A)/Cos^2(A) = tan^2(A)

calc

integrate (3+x)x^(1/2)dx=? please help I have no idea how to integrate this problem

Algebra

Write an equation for the translation of the function. y = cos x; translated 6 units up A. y = cos x- ­ 6 B. y = cos(x + 6) C. y = cos x + 6 D. y = cos(x ­ 6) I think its B or c..

math

if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2

plz integrate

how do u integrate 1+u/3u+2u^2 please help me get started ...tnk u

MATHS...PLEASE HELP

what do you get when you: integrate 10sin^4xcosx dx when you integrate 9x^2e^6x^3 dx

algebra

Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will help. in my algebra ...

Calculus

Integrate (1/2)sin(x^(1/2))dx. I've tried using u-substitution, with u=sin(x^(1/2)). du would then = ((1/2)x^(-1/2))(cos(x^(1/2))). As you can see, this only make the problem more complicated. I don't get what to do. Thank you in advance!

Trigonometry

There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these standard trig formulas? What are they called...

Precal

I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - sin^6 A - cos^6 A + 2sin^3 A cos^3 A - 2sin^3 ...

Calc

Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the x-axis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now, from top to bottom, ...

Math

Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

Cos-Derivative

y= (cos^3 x) (cos 3x) I got -3 sin(3x) cos^3x - 3 sin(x) cos (3x) cos^2 (x) using the product rule Is this right? Thanks.

Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v - u) = cos u cos v + ...

Calc II

For the following question, we need to find the length of the polar curve: r= 2/(1-cosx) from pi/2 </= x </= pi dr/dx= -2sinx/(1-cosx)^2 therefore the length would be expressed as follows: the integral from pi/2 to pi of (sqrt)[(2/(1-cos))^2 + (-2sinx/((1-cosx)^2))^2 ...

Math

Prove each identity: a) 1-cos^2x=tan^2xcos^2x b) cos^2x + 2sin^2x-1 = sin^2x I also tried a question on my own: tan^2x = (1 – cos^2x)/cos^2x R.S.= sin^2x/cos^2x I know that the Pythagorean for that is sin^2x + cos^2x That's all I could do.

math

the question asks to integrate cos(t)/(5sin(t)+8)^2 the answer i got was xcos(t)/(5sin(t)+8)^2 i think the x is wrong but i am not sure what i am doing wrong...help please.

Math

Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

Math

Find the exact value of cos 1 degree + cos 2 degrees + cos 3 degrees + ... + cos 357 + cos 358 degrees + cos 359 degrees.

Trig

Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) =Sin-3/5 cos-3/5 = -0.46602 HELP ...

maths

integrate by parts integrate (4+x^2)^1/2

maths

integrate by parts integrate (4+x^2)^1/2

Math - Solving for Trig Equations

Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360 -- cos^2x - 1 = sin^2x -- Attempt: cos^2x - 1 - sin^2x = 0 cos^2x - 1 - (1 - cos^2x) = 0 cos^2x - 1 - 1 + cos^2x = 0 2cos^2x - 2 = 0 (2cos^2x/2)= (-2/2) cos^2x = -1 cosx = square ...

Trig Help!

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula? This is what I got so far.. cos 2(π/6) = cos (π/6 + π/6) = (cos π/6)(cos π/6) - (sin π/6)(sin π/6) = cos^2...

Math (Integrals) (Volume of Revolution Setup)

I am supposed to find the area of the region given two boundaries and two functions revolving about the x axis. x = 0 x = pi/2 y = cos(x/2) y = sin(x/2) Graphing those two functions made me select to use the washer method. Therefore, I set my definite integral to this: pi∫[0...

Math(Please check)

Use the fundamental identities to simplify the expression. tan^2 Q / sec^2 Q sin^2/cos^2 / 1/cos^2 = sin^2 / cos^2 times cos^2 / 1 = The cos^2 cancels out so sin^2 is left. Is this correct?

Pre-Cal (Trig) Help?

The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost on how to even begin this problem. I do know ...

AP Calc B/C

Find the arc length of one arch of the sine curve. I started it by doing y=sinx, y'=cosx arc length= integral of sqrt(1+cos^2x)dx from pi/2 to 3pi/2 but I don't know how to integrate that! Thank you!

Trig. Law of Cosines

Show that any triangle with standard labeling... a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c I don't get it. Can someone please help me. Start here with the law of cosines: a^2 = b^2 + c^2 -2bc Cos A b^2 = a^2 + c^2 -2ac Cos B c^2 = a^2 + b^2 - 2ab Cos C Add ...

Math

Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- I know the answer is an identity, and when graphed, it looks like cot x. I just don't know how to get there. I tried multiplying each side by its conjugate, but I still feel stuck. This is what I have so ...

Calculus Indefinite Intergral

I need help with integrating these two problems. Im stuck. 1. integrate (sin^-1)dx/((1-x^2)^3/2) sin^-1 aka arcsin 2. integrate dx/((1-x^2)^3/2) by using 1/z Any and all help will be appreciated!

integral calculus

Integrate (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x))dx thanks

integral calculus

integrate: [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) )] - sin (x)

math

Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t) - cos(t) + C s(t) = -cos(t) - sin(t) + Cx + D 6 = v(0) = sin(0) -cos(0) + C C=7 2= s(0) = -...

Math

Show that for real x that {[cos x + 2 sin x + 1]/[cos x + sin x] } cannot have a value between 1 and 2. Let y = [(cos x+2 sin x + 1)/(cos x + sin x) ] y(cos x + sin x) = (cos x + 2 sin x + 1) sin x(y-2) + cos x(y-1)=1 , I just feel that this isn't the way to do this.. Any ...

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

1) Integrate (e^x+x)^2(e^x+1) dx 2) Integrate xe^x2 dx Let u=(e^x+x) du=(e^x +1) dx I will be happy to critique your work or thinking. You are posting work for me to do, and I am not inclined to do that, it will not help you for me to do it. I think I gave you strong hints on ...

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