Question

(1) Evaluate the following integrals. \begin{align} (a) \int_0^{\frac{\pi}{4}} (x - 1) \cos 2x dx\\ (b) \int \frac{1}{(x^2 + 9)^2} dx \end{align}

          (1) Evaluate the following integrals.
\begin{align*}
(a) \int_0^{\frac{\pi}{4}} (x - 1) \cos 2x dx\\ (b) \int \frac{1}{(x^2 + 9)^2} dx
\end{align*}

(1) Evaluate the following integrals.

(a) ∫0^(π)/(4) (x - 1) cos 2x dx
(b) ∫(1)/((x^2 + 9)^2) dx

Added by Yolanda V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Justin Swantek

Step 1

First, let's use the identity cos^2(x) = (1 + cos(2x))/2 to rewrite the integral: ∫(x - 1)cos^2(x)dx = ∫(x - 1)(1 + cos(2x))/2 dx Show more…

Show all steps

Thanks for your feedback!

Evaluate the following integral: âˆ«(x - 1)cos^2(x)dx

Play audio

Feedback

Justin Swantek and 63 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Question

(1) Evaluate the following integrals. \begin{align*} (a) \int_0^{\frac{\pi}{4}} (x - 1) \cos 2x dx\\ (b) \int \frac{1}{(x^2 + 9)^2} dx \end{align*}

Please give Ace some feedback

(1) Evaluate the following integrals. \begin{align} (a) \int_0^{\frac{\pi}{4}} (x - 1) \cos 2x dx\\ (b) \int \frac{1}{(x^2 + 9)^2} dx \end{align}