ok!!INt Parts Question!!!

E

EvoRevolution

Member

Mar 25, 2009

#1

show that:

opps soz

Last edited: Mar 25, 2009

tommykins

i am number -e^i*pi

Mar 25, 2009

#2

check your original integral please.

T

Timothy.Siu

Prophet 9

Mar 25, 2009

#3

just make it S sin x. sin^n-1x dx and do it by parts.

$I_n=\displaystyle\int_{0}^{\frac{\pi}{4}}\sin^nx\,dx\\\\u = \sin^{n-1}x, du = (n-1)\sin^{n-2}x \cos x\,dx\\dv = \sin x\,dx, v = -\cos x\\\\I_n=\left [-\cos x\sin^{n-1}x\right ]_{0}^{\frac{\pi}{4}}+(n-1)\displaystyle\int_{0}^{\frac{\pi}{4}}\sin^{n-2}x \cos^2x\,dx\\\\= -2^{-\frac{1}{2}}2^{-\frac{n-1}{2}}+(n-1)\displaystyle\int_{0}^{\frac{\pi}{4}}\sin^{n-2}x (1-\sin^2x)\,dx\\\\=-2^{-\frac{n}{2}}+(n-1)I_{n-2} - (n-1)I_n\\\\(n-1+1)I_n= -2^{-\frac{n}{2}}+(n-1)I_{n-2}\\\\I_n = \dfrac{-2^{-\frac{n}{2}}+(n-1)I_{n-2}}{n}$

ok!!INt Parts Question!!! (1 Viewer)

EvoRevolution

Member

tommykins

i am number -e^i*pi

Timothy.Siu

Prophet 9

Trebla

Administrator

Users Who Are Viewing This Thread (Users: 0, Guests: 1)