Posted by **Kerry-Ann** on Wednesday, January 15, 2014 at 10:51pm.

In=∫ x^nSinx dx....with the limits π/2 and 0

i found that In would be equal to n(π/2)^(n-1) -n(n-1) In-2

how do i deduce the value of I4? where n=4

- Pure Mathematics -
**Steve**, Thursday, January 16, 2014 at 12:49am
you need to do integration by parts.

∫x^4 sinx dx

u=x^4

du = 4x^3 dx

dv = sinx dx

v = -cosx

∫x^4 sinx = -x^4 cosx + 4∫x^3 cosx dx

Now do all that again for each resulting integral, and the powers of x descends until you are left with just ∫sinx dx

Then just add all the pieces together.

Hmmm. I think you can save yourself some work. At x=0 all the terms with powers of x and sinx vanish.

at x=π/2 all the terms with cosx vanish (odd powers of x).

## Answer this Question

## Related Questions

- Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...
- Calculus - How do I find the critical values? y= 4/x + tan(πx/8) What I ...
- Math, please help - Which of the following are trigonometric identities? (Can be...
- Trig - find all solutions to the equation √3 csc(2theta)=-2 Would the ...
- Math - Evaluate *Note - We have to find the exact value of these. That I know to...
- physics - 1.∫ csc (u-π/2) cot (u-π/2) du. 2.∫ sec^2(3x+2)...
- PreCalc - Graph y=2csc(x-π) New period that I solve for 0<x-π<2...
- mathematics - ∫▒dx/(x√(2x^2+5x+1)) 2. ∫▒dx/(x&#...
- calculus - 1. what trig function has an amplitue of 1 and negative values for ...
- Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...

More Related Questions