New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

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

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Calculus with Analytic Geometry II

by: Elaina Osinski

Calculus with Analytic Geometry II MATH 141

Marketplace > Pennsylvania State University > Mathematics (M) > MATH 141 > Calculus with Analytic Geometry II
Elaina Osinski
Penn State
GPA 3.88

Michael Tepper

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Michael Tepper
Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 0 page Class Notes was uploaded by Elaina Osinski on Sunday November 1, 2015. The Class Notes belongs to MATH 141 at Pennsylvania State University taught by Michael Tepper in Fall. Since its upload, it has received 24 views. For similar materials see /class/232999/math-141-pennsylvania-state-university in Mathematics (M) at Pennsylvania State University.

Similar to MATH 141 at Penn State


Reviews for Calculus with Analytic Geometry II


Report this Material


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: 11/01/15
Math 141 Calculus with Analytic Geometry II Penn State University H E0 9 F 01 on Fall 2006 Sections 12161819 Strategy for Integration i Table of Integration Formulas pl 542 1141718 If your integral falls into this category then consider yourself luckyi At this point in your Calculus career very rarely will this be the case initiallyi Most the following methods though will rely on your knowledge of these integrals at some point so make sure you commit them to memory Simplify the Integrand There are countless ways in which you can algebraically simplify an integrand In many cases some creativity is required but the following methods should serve you well a Expand integrand eigi 17 z dz fz 7 z2 W 7 z32 dz b Rationalize the denominator eigi f dz f dz fxz l W dz c Apply a trigonometric identity eigi sin2z dz fl cos2z dz Substitution not including trigonometric substitution fyry r dz 7 fltugt du In general we are looking for a composition of functions But also keep an eye out for a function gz where g zdz appears in the integrand as well Let u g z and don7t forget about du g z dzi Remember substitution is preferable to trigonometric substitution and partial fractions For example both of the following integrals can be computed using the substitution u l 7 z While a trig substitution can be used for the rst integral and partial fractions can be used for the second you7ll save a lot of time and energy using the appropriate substitutioni z l 7 z2 udvuv7vdu This method is useful for integrating inverse functions or products of any two or more of the following types of functions polynomial trigonometric exponential logarithmic and inverse dz Integration by Parts Make sure that you know how to integrate dv and v dui If not select a different set of parts u and dvi If you are integrating an inverse function let u equal the inverse function and let dv dzi i Classify the Integrand a Trigonometric lntegrals sin z cosmz dz ftan z secmz dz fsinnz cosmz dz b Trigonometric Substitution integrals involving m m or W c Rational Functions dz where pz and qz are polynomials d Radicals integrals involving m try the substitution u W i If at rst you don t succeed try again Sometimes a combination of the above methods may be required For example you might have to use a substitution before being able to use integration by parts In many trigonometric substitution problems eventually you will need to evaluate a trigonometric integrali If you get stuck try a substitution or integration by parts Applied correctly it will always lead to a different way of looking at the same prob emf Problems 180 from Stewarfs Calculus7 page 546547 H sin z sec z f4tz3nz d9 to z tan39 d9 CA3 2 2 f0 Wis dt f s7 d9 1 mafia 5 fil 8171127 dy fzcscz cotz dz 533 N z 13T41n39r dz 4 m 8 f0 z274z175 d1 f z71 d1 z274z5 50 10 dz z sin3z cos5z dz z fsinz coscosz dz HH OH 13 W dz 1lnz z W dz H g 12 E 15 f0 Wdz Q z2 16 0 dz 17 fzsin2z dz 18 f 1 dt 19 few dz 20 fagE dz 21 ftge m dz 22 fzsin 1z dz 011 38 dz z flnz2 71 dz MM ugtw 25 f 31272 dz z272z78 26 f 3052 dz z372z78 27 footz 1nsinz dz to 00 CAD to CA3 g CA3 on 01 g fW z W dy z f9tan29 d9 z sz tan 1z dz z fexm dz Wdz z fz5e 7 3 dz fzxAllzj f 2W z fsin Q dt A 1 dw 2 z f32 z2 7 4z dz fz2z71 dz 2z3 zfx372z7z2 dz fW214COLT dz 7r4 47mm z fil z8 sinz dz z fsin4z cos3z dz z M4 0052 9 tan29 d9 0 z few4 tan5 9 sec3 9 d9 dz 1e lie dz za z 1 H a dz fzjf zldr dz 1 f W dz dz de NOT RELEVANT z sinz2 dz 01 0 mm 9 7 N to 00 0 WW zlnz fHdI 1 JW 3 u31 f2 uLu d fw z f 12 dz f z z44z23 zfi dt dz 2 fzxgzc dz fz21n1z dz f d1 fmdz 4 z fz1016 dI ES szdz f ze Z dz fWS lntanz dz 7r4 75am cosz dz fs cangx dt 1 dz f 1n1 d1 dz 1 f Wm d1 f 1 dz e 7equot z fsinz sin2z sin3z dz z z2 7 bz sin2z dz z L dz z 1z3 secz cos2z f 451nzsecz d9 z fzsin2z cosz dz f sinz cosz d1 sin zcos z


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

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

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

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

Parker Thompson 500 Startups

"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."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.