Download presentation

Presentation is loading. Please wait.

Published byJason Morris Modified over 5 years ago

1
Integration by parts Product Rule:

2
Integration by parts Let dv be the most complicated part of the original integrand that fits a basic integration Rule (including dx). Then u will be the remaining factors. Let u be a portion of the integrand whose derivative is a function simpler than u. Then dv will be the remaining factors (including dx). OR

3
Integration by parts u = x dv= e x dx du = dx v = e x

4
Integration by parts u = lnx dv= x 2 dx du = 1/x dx v = x 3 /3

5
Integration by parts u = arcsin x dv= dx v = x

6
Integration by parts u = x 2 dv = sin x dx du = 2x dx v = -cos x u = 2x dv = cos x dx du = 2dx v = sin x

7
8.2 Trigonometric Integrals Powers of Sine and Cosine 1. If n is odd, leave one sin u factor and use for all other factors of sin. 2. If m is odd, leave one cos u factor and use for all other factors of cos. 3. If neither power is odd, use power reducing formulas:

8
Powers of sin and cos

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google