February 21, 2017

Homework Help: Calculus AP

Posted by Vicky on Thursday, August 2, 2012 at 5:59pm.

hi again
im really need help
TextBook: James Stewart:Essential Calculus, page 311. Here the problem #27: First make a substitution and then use integration by parts to evaluate the integral.
Integral from sqrt(pi/2) TO sqrt(pi)of θ^3 cos(θ^2)dθ.

i did my problem: let t=θ^2 then dt= 2θdθ.

∫θ^3cos(θ^2)dθ = ∫1/2 t cos t dt

=1/2∫tcostdt -> let u=t, dv=cost dtthen du = 1, v= sin t

=1/2[tsint-∫sint dt]
=1/2 tsint + 1/2 cos t + c.. reminder t=θ^2
=1/2 θ^2 sin(θ^2)+ 1/2 cos(θ^2) + c

so i got stuck and don't know how to solve with sqrt(pi) and sqrt(pi/2)

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