### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# LinearAnalysis MATH287

GPA 3.8

### View Full Document

## 39

## 0

## Popular in Course

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Leopoldo Rutherford on Sunday October 11, 2015. The Class Notes belongs to MATH287 at Cuesta College taught by RobertSchwennicke in Fall. Since its upload, it has received 39 views. For similar materials see /class/221241/math287-cuesta-college in Mathematics (M) at Cuesta College.

## Similar to MATH287 at

## Popular in Mathematics (M)

## Reviews for LinearAnalysis

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/11/15

Math 287 Partial Fraction Decomposition X In order to integrate an integrand of the form it is often necessary to decompose this fraction into a sum of simpler fractions The process used to accomplish this is called partial fraction decomposition STEP 1 Divide if improper If N x Dx is an improper fraction that is if the degree of the numerator is greater than or equal to the degree of the denominator then divide then rewrite the fraction as a polynomial plus the fraction N1 x Dx where the polynomial is the quotient of N x Dx and N1 x is the remainder of N x Dx Then apply the following steps to the proper fraction N1 x Dx STEP 2 Factor the denominator Completely factor the denominator Dx into factors of the form px q and CDC2 bx C where ax2 bx C is irreducible STEP 3 Linear factors For each factor of the form px q the partial fraction decomposition must include the following sum A 1 22 mm px q px q px q of m fractions STEP 4 Quadratic factors For each factor of the form axz bx C the partial fraction decomposition must include the leC1 BzxC2 anCn ax2 bxc ax2 bxc2 ax2 bxc following sum of 71 fractions Practice Evaluate the following integrals J x3 2 Jx212x12dx x24x5 I x34x 4 m4 2x 5 2s1nx 3 I dx 439 i z 1x 4x x 0 c0sxc0s x1 Math 287 Trigonometric Substitution Your text contains a table on integrals in the inside front cover Formulasl 17 42 7 45 can be generated using a technique called trigonometric substitution These formulas apply to integrands which contain expressions of the form V612 x2 V a2 x2 or sz a2 The idea behind trigonometric substitution is to write the expression under the radical as a square and thereby remove the radical We will use two identities from trigonometry to accomplish this cos2 9 Sin2 9 l and l tanz t9 sec2 9 1 Make the substitution x a sin 9 with 9 restricted to the values S 9 S Then Val x2 xa2 a2 sin2 9 Jaz sin2 9 wa2 cos2 9 alcos 6 acost9 and dx a COS 9 The triangle to the right can help you seethat whiz x2 ac0st9 a x Ma et e sust1tut10n x atanH with 9 restricted to the values S 9 S Then Val x2 ch2 a2 tan2 9 aZ1tan2 t9 xa2 sec2 9 alsect9 asect9 and dx a sec2 9 The triangle to the right can help you seethat Val x2 asect9 3 Make the substitution x asecQ with 9 restricted to the values 0 S 9 S or 7239 S 9 S37 Then lxz a2 ch2 sec2 6 a2 czzsec2 9 1 1a2 tan2 9 altant9 atant9 and dx a sec 0 tan 0 The triangle to the right can help you seethat xxz a2 atant9 x a Practice Use the techniques above to compute the integrals l 2 IV4x2dx

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.