Exam review 2.pdf - Exam 2 Review Questions 1 Know how the...

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Exam 2 Review Questions 1. Know how the integral represents area. Know how to find the area of a region using integrals. 2. What is the area between x 5 and x 1 5 in the upper-right quadrant? 3. What is the area between the curves x = y 5 - y and x = 8 y 3 - y where x > 0? 4. What fraction of the area of the rectangle given by the x -axis, y -axis, x = a and y = b · a n , is below the curve y = b · x n ? (Hint: in the end your answer should depend only on n , not on a or b .) 5. Understand the idea and formula behind the washer and disk methods. 6. Calculate the volume of a surface of revolution given by revolving the area between the two functions f ( x ) = x 2 and g ( x ) = - x 2 bounded by x = 0 and x = 2 around the line y = - 4. Use the washer method. (Hint: the answer is 128 π 3 .) 7. Calculate the above volume, but use the shell method instead. (Hint: there are 2 pieces, one piece where y 0 and one piece where y 0, giving two different integrals. The volume should be the same as above.) 8. When you use the washer method for a surface revolved around the y

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