1 Math 20B Midterm 2 Review Outline Basic Information for the Midterm Exam: Themidterm is cumulative but will have emphasis on Sections 7.1-7.4, 7.7, 7.8, Supplement 2.2, 3.4, 4.6, 11.1-11.4; it will not focus too much on any particular topic. However, in a math class, it all builds upon itself. You will notbe allowed a calculator on the exam, so please do not bring one. You shouldbring a number two pencil. (You can bring more than one if you feel so inclined.) You are permitted a handwrittenreference sheet on the exam (8.5 x 11 inches). You can put whatever you feel is important on it (see the rest of this document for ideas.) Please, do not bring anything more than this.We reserve the right to place your backpacks in the front of the class. You don’t need to worry about bringing a blue book, as you will be able to write directly on the exam. The exam will be held on Friday, November 16th, 2007, in class (LEDDEN AUD). You should have sufficient time to go back through your work and check your math. Remember, does your answer make sense? (Draw a picture/plug numbers in.)
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Math 20B Midterm 2 Review Outline2 Section 7.1: Integration By Parts Know how to integrate using integration by parts The formula is udvuvvdu=−∫∫. Know how to choose uand dv(following LIPET) - see the chart to the right - ex. (i)40sin(2 )xx dxπ∫; (ii) 161ln( )xx dx∫; (iii) 31ln( )exx dx∫; (iv) 130zzedz−∫; (v) 2130xx edx∫; (vi) 3220cos()xxdxπ∫- ex. Evaluate 3/2ln( )xx dx∫; ln( )xdxx∫; 2sin( )cos ( )xxx dx∫Section 7.2: Trigonometric Integrals Know how to use integration by parts to find integrals of sinn(x) and cosn(x) Know the strategy for evaluating sinm(x)cosn(x) for different combinations of mand nKnow the trig identities 21cos(2 )cos ( )2xx+=and 21cos(2 )sin ( )2xx−=Know how to do something similar for tanm(x)secn(x) - ex. Evaluate 4440sectandπθθ θ∫; 35sin ( )cos ( )xx dx∫; 1120cos( )sin( )xx dxπ∫- ex. Find the average value of 2( )1f xx=−on [-1, 1]. Know the sum-to-product and product-to-sum formulas for sine and cosine - 12sincossin()sin()ABABAB=−++- 12sinsincos()cos()ABABAB=−−+- 12coscoscos()cos()ABABAB=−++Supplement 2.2: Integrating Products of Sines, Cosines and Exponentials Know how to use the formulas for sine and cosine from Supplement 1.2 to express sine and cosine in terms of exponentials - ex. Evaluate 2cos( )ixex dx∫; 2sin(4 )ixex dx−∫; 5cos(3 )ixex dx∫- ex. Use complex exponentials to evaluate cos(2 )sin(7 )xx dx∫and write the result in terms of trigonometric functions. - ex. Evaluate55()ixixi eedx−−∫and ()ixixeedx−+∫; write the result using only real-valued functions.udvLIPETonoxrgvlpisyg→