{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3Bstudyguide

3Bstudyguide - able to compute both types The following...

This preview shows pages 1–2. Sign up to view the full content.

This is a study guide for the second Math 3B midterm. It indi- cates which types of problems you may be expected to answer on the midterm, with instructions on where to find these topics in the Stewart calculus book. Plenty of examples can be found in the exercises at the end of each sec- tion of any calculus book. Although many of these may be a little more complicated than problems on the exam, they are excellent practice. In general, the best way to learn the techniques of integration is to practice a lot of problems. This document is intended to make some supplementary points. No books, notes, index cards, calculators of any kind are allowed. To the extent that you need trigonometric identities, these will be provided for you on the cover sheet. You are still responsible for knowing all the basic antiderivatives listed on the first page of the review sheet for Exam I (still posted on GauchoSpace. Remember that our techniques of integration apply to de- nite integrals (areas) as well as indenite integrals (antiderivatives).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: able to compute both types. The following identities will be given to you on the exam. I might even put more if I’m feeling generous! • sin 2 x + cos 2 x = 1 • tan 2 x + 1 = sec 2 x • cos 2 x = 1 2 (1 + cos(2 x )) • sin 2 x = 1 2 (1-cos(2 x )) • sin(2 x ) = 2 sin( x ) cos( x ) Techniques you need to know: • u-substitution. For example, Z x ( x 2 + 1) 3 dx See Stewart 5.5 for more. • Integration by parts. For example, Z x sin( x ) dx See Stewart 7.1 for more. • Partial fractions. For example, Z x 2 + 3 x 3-2 x 2-3 x dx See Stewart 7.4 for more. • Inverse/trigonometric substitutions. For example, Z 1 x 2 √ x 2-16 dx See Stewart 7.3 for more. • Strategy for integrating i.e., identifying which of the above techniques to apply to a given integral and combining the above techniques to compute integrals. See Stewart 7.5. • You also need to know about improper integrals. For example Z ∞ 2 1 x 2 dx See Stewart 7.8 for more....
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern