Calculus AP
posted by Vicky .
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)

Calculus AP 
MathMate
Up to 1/2∫tcostdt, you're OK.
After that, you need to integrate by parts.
I=(1/2)∫t cos(t)dt
=(1/2)[t sin(t)  ∫sin(t)]
=(1/2)[t sin(t) + cos(t)
To evaluate the definite integral, remember to adjust the limits accordingly, i.e.
from x^2 to t
sqrt(π/2)^2=π/2
sqrt(π)^2=π
I get (π+2)/4
Respond to this Question
Similar Questions

Calculus
so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would … 
Math  Calculus
The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below.  a … 
Math  Trig Substitution
How can I solve the integral of x^3√(9x^2) dx using trigonometric substitution? 
Calculus II
Evaluate using usubstitution: Integral of: 4x(tan(x^2))dx Integral of: (1/(sqrt(x)*x^(sqrt(x))))dx Integral of: (cos(lnx)/x)dx 
Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find … 
Calculus
First make a substitution and then use integration by parts to evaluate. The integral of (x^9)(cos(x^5))dx What do you substitute first? 
Calculus
First make a substitution and then use integration by parts to evaluate. The integral of (x^9)(cos(x^5))dx What do you substitute first? 
PreCalculus
If θ represents an angle such that sin2θ = tanθ  cos2θ, then sin θ  cosθ = A. √2 B. 0 C. 1 D. 2√2 What equation can I use to solve this problem? 
Trigonometry
There are four complex fourth roots to the number 4−4√3i. These can be expressed in polar form as z1=r1(cosθ1+isinθ1) z2=r2(cosθ2+isinθ2) z3=r3(cosθ3+isinθ3) z4=r4(cosθ4+isinθ4), … 
Math
Evaluate the integral from [sqrt(pi/2), sqrt(pi)] of x^3*cos(x^2) by first making a substitution and then using integration by parts. I let u = x^2 and du= 2x dx but then it doesn't equal that in the equation?