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exam2review - Math 20B Midterm 2 Review Outline Basic...

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1 Math 20B Midterm 2 Review Outline Basic Information for the Midterm Exam: The midterm 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 not be allowed a calculator on the exam, so please do not bring one. You should bring a number two pencil. (You can bring more than one if you feel so inclined.) You are permitted a handwritten reference 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 16 th , 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 Outline 2 Section 7.1: Integration By Parts Know how to integrate using integration by parts The formula is udv uv vdu = . Know how to choose u and dv (following LIPET) - see the chart to the right - ex. (i) 4 0 sin(2 ) x x dx π ; (ii) 16 1 ln( ) x x dx ; (iii) 3 1 ln( ) e x x dx ; (iv) 1 3 0 z ze dz ; (v) 2 1 3 0 x x e dx ; (vi) 3 2 2 0 cos( ) x x dx π - ex. Evaluate 3/2 ln( ) x x dx ; ln( ) x dx x ; 2 sin( )cos ( ) x x x dx Section 7.2: Trigonometric Integrals Know how to use integration by parts to find integrals of sin n ( x ) and cos n ( x ) Know the strategy for evaluating sin m ( x )cos n ( x ) for different combinations of m and n Know the trig identities 2 1 cos(2 ) cos ( ) 2 x x + = and 2 1 cos(2 ) sin ( ) 2 x x = Know how to do something similar for tan m ( x )sec n ( x ) - ex. Evaluate 4 4 4 0 sec tan d π θ θ θ ; 3 5 sin ( )cos ( ) x x dx ; 11 2 0 cos( )sin ( ) x x dx π - ex. Find the average value of 2 ( ) 1 f x x = on [-1, 1]. Know the sum-to-product and product-to-sum formulas for sine and cosine - [ ] 1 2 sin cos sin( ) sin( ) A B A B A B = + + - [ ] 1 2 sin sin cos( ) cos( ) A B A B A B = + - [ ] 1 2 cos cos cos( ) cos( ) A B A B A B = + + 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 2 cos( ) i x e x dx ; 2 sin(4 ) i x e x dx ; 5 cos(3 ) i x e x dx - ex. Use complex exponentials to evaluate cos(2 )sin(7 ) x x dx and write the result in terms of trigonometric functions. - ex. Evaluate 5 5 ( ) i x ix i e e dx and ( ) ix ix e e dx + ; write the result using only real-valued functions. u dv L I P E T o n o x r g v l p i s y g
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