Saturday

March 28, 2015

March 28, 2015

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

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 dont know how to solve with sqrt(pi) and sqrt(pi/2)

- Calculus AP -
**MathMate**, Thursday, August 2, 2012 at 10:00pmUp 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

**Answer this Question**

**Related Questions**

Calculus - How do I evaluate this integral: x^9cos(x^5)dx Hint: First make a ...

Calculus - First make a substitution and then use integration by parts to ...

Calculus - First make a substitution and then use integration by parts to ...

calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...

Calculus - Use either substitution or integration by parts to evaluate the ...

Calculus - I have two questions, because I'm preparing for a math test on monday...

Calculus Please Help2 - Evaluate the integral by using substitution. Use an ...

calculus - Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = ...

Calculus II - Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx ...

Calculus Please Help - Evaluate the indefinite integral Note: Use an upper-case...