Calculus AP
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)

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)/4posted by MathMate
Respond to this Question
Similar Questions

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.  
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 
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? 
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? 
Calculus URGENT test tonight
Integral of: __1__ (sqrt(x)+1)^2 dx The answer is: 2ln abs(1+sqrt(x)) + 2(1+sqrt(X))^1 +c I have no clue why that is! Please help. I used substitution and made u= sqrt(x)+1 but i don't know what happened along the way! Your first 
Math  Trig Substitution
How can I solve the integral of x^3√(9x^2) dx using trigonometric substitution? ? ∫ x^3√(9x^2) dx So then I know that x = 3sinθ dx = 3cosθdθ When I substitute, it becomes ∫ (3sinθ)^3 * 
Calculus
Find the volume of the solid whose base is the region in the xyplane bounded by the given curves and whose crosssections perpendicular to the xaxis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, 
calculusintegration!
should i use substitution?? if yes how should should i use it? plz i need some directions? k plz someone?...so far i used trig. substitution. i got a=8, so i used x=asin(è)so according to this substitution i got x=8sin(è) and 
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), 
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