Download presentation

Presentation is loading. Please wait.

Published byUlises Potterton Modified over 3 years ago

1
Clicker Question 1 What is ? – A. 1 / (1 + x 2 ) + C – B. x / (1 + x 2 ) + C – C. sin( ) – D. (1 + x 2 ) + C – E. (1 + x 2 ) / x + C

2
Clicker Question 2 What is ? – A. 3/2 – B. / 6 – C. 10 / (9 3) – D. / 6 + 1 / (9 3) – E. 5 / 3

3
Clicker Question 3 How do you feel about trig integrals and trig substitutions? – A. Love em! ( Right Answer!) – B. %&*$%#@*& – C. Whats trig?

4
Partial Fraction Technique Recall what a rational function is. Question: It is possible to anti-differentiate any rational function? Answer: Theoretically, yes! – If top has higher (or =) power than the bottom, divide, getting whole and fractional parts. – Factor the bottom into linears and quadratics. – Separate each factor out using partial fraction technique. – Integrate each part using u-subs or trig subs.

5
A simple example (1/(x 2 – 3x – 4))dx – Factor the denominator. – Write A/(x – 4) + B/(x + 1) = 1/(x 2 – 3x – 4) and solve for A and B. – Now we have two separate integrals we can solve.

6
Two More Examples (x 3 / (x 2 +1))dx – This is an improper fraction. So divide first! ((x + 2)/(x 3 + x))dx – If, after factoring, a factor of the denominator is quadratic (as opposed to linear), we need to put Ax + B above it, not just A.

7
Assignment for Monday Hand-in #1 is due at noon. Read Section 7.4. Do Exercises 7, 9, 11, 15 in that section.

Similar presentations

OK

Chapter 7: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals.

Chapter 7: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 4 types of sentences Ppt on swami vivekananda death Ppt on wifi technology free download Ppt on bluetooth based smart sensor networks definition Ppt on ip address classes hosts Ppt on financial services in india Ppt on recycling of waste oil Ppt on data collection methods in research methodology Make a ppt on election system in india Ppt on global marketing management