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# Midterm - x-axis is A 3/10 B 3π/10 C 3π/5 D 10π/3 4(a...

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Midterm Exam (Math 200 A, Fall 06) Solve the following problems. Show all your work in the space under each problem. 1. Answer the following: (15 pts) (a) Evaluate the integral: dx x 2 1 ) 1 1 ( (b) The result you found in (a) describes: A. The length of the arc of the hyperbola x y 1 1 from x = 1 to x = 2. B. The area under the hyperbola x y 1 1 from x = 1 to x = 2. C. The volume by revolution around the x -axis generated by the hyperbola x y 1 1 from x = 1 to x = 2. (c) True or False : 0 ) ( dx x f a a 2. Answer the following: (20 pts) (a) Evaluate the integral: 2 2 1 x x x dx (use substitution method) (b) Evaluate the integral: dx x x cos (use by parts method) 3. (a) The area of the region enclosed by the parabolas 2 2 x x y and 2 x y is: (20 pts) A. 10/6 B. 2/3 C. 1/3 D. 5/6 (b) The volume of the solid obtained by rotating the region bounded by the curves

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Unformatted text preview: x-axis is: A. 3/10 B . 3π/10 C . 3π/5 D . 10π/3 4. (a) Evaluate the integral: dx x x 3 2 cos sin (15 pts) (b) The correct substitution to evaluate the integral 4 2 2 x x dx is: A. sin 2 x B. tan 2 x C. cos 2 x D. sec 2 x (c) The correct partial fraction expansion to evaluate the integral dx x x ) 9 )( 1 ( 10 2 is: A. 9 1 2 x B x A B. 9 1 2 x C Bx x A C. 9 1 2 x Bx x A D. 2 2 ) 9 ( 1 x B x A 5. Evaluate the improper integral: dx xe x (10 pts) 6. The length of the arc of the curve 2 / 3 2 y x from (0,0) to (2,1). (10 pts) 7. Given the curve 3 2 , t t y t t x , with 1 1 t , find ) , ( 2 2 | dx y d . (10 pts)...
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