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


by: Vivien Bradtke V


Vivien Bradtke V
Texas A&M
GPA 3.6

Y. Gorb

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

Y. Gorb
Class Notes
25 ?




Popular in Course

Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Vivien Bradtke V on Wednesday October 21, 2015. The Class Notes belongs to MATH 152 at Texas A&M University taught by Y. Gorb in Fall. Since its upload, it has received 45 views. For similar materials see /class/226007/math-152-texas-a-m-university in Mathematics (M) at Texas A&M University.

Similar to MATH 152 at Texas A&M

Popular in Mathematics (M)




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: 10/21/15
MATH 152 Fall 2008 Yuliya Gorb goermath tamu edu wwwmathtamu edu gorbmath152ia112008html Formula Sheet for Exam 1 Area The area of the region bounded by y and y 91 and the lines 1 a 1 b for continuous functions7 where 2 for all 1 in a z is b Avmemmm Volume H The volume of the solid that lies between planes 1 a 1 b and whose crosssection perpendicular to the 1axis has an area A1 is V ab A1d1 to 1 Disk method The volume of the solid of revolution that lies between planes 1 a 1 b and which is generated by revolving of y around the 17axis is V ab 7rf12d1 i Washer method The volume of the solid of revolution that lies be tween planes 1 a 1 b and which is generated by by revolving of the region between y and y 91 2 around the 17axis is CA3 b v wvwemm m 4 Method of cylindrical shells The volume of the solid generated by the revolving of the region bounded by y 1 a and 1 12 around yiaxis is b V 27TIfIdI Here 1 is the radius of the shell7 is its height Work The work done in moving an object from a to b by the force is W Abf1d1 1 Hook s law f I 7m where k is the spring constant7 z is the displacement from equilibrium position A erage The average of the function on the interval a b is 1 b fave a Mean Value Theorem lf is continous on the interval a b then there exists a number 5 in m 12 such that b mm fcb 7 a Integration by Parts fIy IdI f191f I9IdI udvuv7vdu b b b agmm fltzgtgltzgtla7 f ltzgtgltzgtdz For de nite integrals Trigonometric Integrals ll sinm 1 cos zdz o nis odd n2kl a save one cosine factor b use cos2 I l 7 sin2 I c make substitution u sin I du cos zdz o mis odd m2kl a save one sine factor b use sin I l 7 cos2 I c make substitution u cos I du 7 sin zdz 0 both m and n are even m 216 n 2k use 2 cos2 I lcos 21 sin I l7cos 21 sinz cosz sin 21 2 tanm 1 sec zdz o n is even n 216 a save a factor of sec2 1 b use sec2 1 1tan2 z c make substitution u tan 1 du sec2 zdz o mis odd m2k1 a save a factor of sec 1 tanz b use tan2 1 sec 1 71 c make substitution u sec 1 du sec 1 tan zdz Important Trigonometric Identities sinz 1 tanz secz cscz cos 1 cos 1 sin I sin2ercos2117 tan211sec21 2 cos I 1 cos 217 sin2 I 17 cosZI7 sinZI 2sinzcosz d 2 d 7tanz sec 1 7secz secztanz dz dz tanzdzlnlseczl07 seczdzln secztanzlC 1 sinz cosy sin1 y Sinz 1 cosz cosy cos1 y cosz sinz siny cosz 7 y 7 cosz Substitution M Qz Partial Fraction Decomposition for rational function fx Where Pz and are polynomials 1 1f deg Pz 2 deg then use long division of two polynomials to get P I R I Where Rz is a remainder such that deg Rz lt deg and 51 is a quotient 2 CA3 Express the proper rational function Factor the denominator as a product of linear factors of the form az b and irreducible quadratic factors of the form 0412 121 c Where b2 7 4ac lt 0 31 QW as a sum of partial fractions of the form AIB or a12 121 cm L ax bk a if is a product of distinct linear factors ie mm b1agz 122 l l akz bk then there exist constants A1 A2 Ak such that Rm QW A1 alz 121 7a2xb2m Ak akz bk if is a product of linear factors some of Which are repeated elgl has a factor ax by the corresponding partial fractions are A1 A2 A2 azbazb2 uazbi if contains irreducible quadratic factors none of Which is re peated ilel a112 1211 cl 212 1221 62Hiam12 bmz cm then there exist constants A1 Am and B1 H l Bm such that 131 7 A11 B1 A21 B2 Amz Bm 7 a112blzcl l a212bgz02 l l am12bmzcm if contains a repeated irreducible quadratic factor elgl has a factor ale 1211 01V Where b2 7 4ac lt 0 then the corresponding partial fractions are A11 B1 A21 B2 Air BI a12 121 5 a12 121 c2 Hi a12 121 c


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

Jim McGreen Ohio University

"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."

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.