Maths - Integration by parts

posted by .

Integral x^2 sin(x) dx

  • Maths - Integration by parts -

    Let I = ∫x^2 sinx dx

    u = x^2
    du = 2x dx

    dv = sinx
    v = -cosx

    ∫u dv = uv - ∫v du
    = -x^2 cosx + ∫2x cosx dx

    now, for ∫x cosx dx,

    u = x
    du = dx

    dv = cosx dx
    v = sinx

    I = -x^2 cosx + 2(x sinx - ∫sinx dx)
    = -x^2 cosx + 2x sinx + 2cosx + C
    = 2x sinx + (2-x^2)cosx + C

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. integration by parts

    s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1)) = ln(2x+1)x- s x [(2x+1)'/ (2x+1)] dx = ln(2x+1)x- s x [(2)/ (2x+1)] ?
  2. trig integration

    s- integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1-cos (4x)] dx, but then i'm confused. The indefinite …
  3. Integral

    That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten integral …
  4. calc

    evaluate the integral: y lny dy i know it's integration by parts but i get confused once you have to do it the second time Leibnitz rule (a.k.a. product rule): d(fg) = f dg + g df y lny dy = d[y^2/2 ln(y)] - y/2 dy ----> Integral …
  5. Math/Calculus

    How would I integrate the following by parts: Integral of: (x^2)(sin (ax))dx, where a is any constant. Just like you did x^2 exp(x) below. Also partial integration is not the easiest way to do this integral. You can also use this method. …
  6. Calculus II

    Evaluate the integral using method of integration by parts: (integral sign)(e^(2x))sin(5x)dx
  7. math

    I'm trying to find the convolution f*g where f(t)=g(t)=sin(t). I set up the integral and proceed to do integration by parts twice, but it keeps working out to 0=0 or sin(t)=sin(t). How am I supposed to approach it?
  8. double integral

    1. Sketch the region of integration & reverse the order of integration. Double integral y dydz... 1st (top=1, bottom =0)... 2nd(inner) integral (top=cos(piex), bottom=(x-2)... 2. Evaluate the integral by reversing the order of integration. …
  9. Calculus Problem

    I need to find the integral of e^(2x)sin(3x) I used integration by parts and I let u=e^2x and dv=sin(3x) My final answer was (-3/8)(e^(2x))(cos(3x)) - (1/8)(e^(2x))(sin(3x)) but it's wrong. Please help!!
  10. Integration by Parts

    integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be -pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=-cos(t) i integral sin(t)e^(it)dt= -e^(it)cos(t)+i*integral cost(t)e^(it)dt …

More Similar Questions