# mid1f - R b a f y dy Do not evaluate the integral(s(c(4 pts...

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1. (7 pts) Find the function F ( x ) such that F 0 ( x ) = x 3 x + 1 and F (0) = 0. 2. (8 pts) Use the Midpoint Rule (taking y -values at the midpoints of the intervals) with n = 3 subdivisions to ±nd the approximate value of Z 6 0 x 2 + 5 x 3 + 1 dx . Give your answer to two decimal places (to the nearest .01).

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3. (5 pts) Let f ( x ) = Z 2 x +7 0 dt t 4 + 9 . Compute f 0 ( x ). 4. (8 pts) Compute Z π/ 3 π/ 6 sin 3 x 2 + cos 3 x dx .
5. Let R be the region above the x -axis, above the curve y = 1 4 ( x 2 - 1), and below the line y = 2 3 x . (See the drawing.) (a) (3 pts) Express the area of R as an integral, or sum of integrals, of the form R b a f ( x ) dx . Do not evaluate the integral(s). (3,2) R (b) (3 pts) Express the area of R as an integral, or sum of integrals, of the form

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Unformatted text preview: R b a f ( y ) dy . Do not evaluate the integral(s). (c) (4 pts) Evaluate the integral(s) in either (a) or (b) [take your pick] to Fnd the area of R . 6. Let S be the region bounded by the curve y = e x/ 3 , the line y = e , and the y-axis. (See the drawing.) (a) (8 pts) Find the volume of the solid obtained by revolving S about the x-axis. (3,e) S (b) (4 pts) Set up an integral that represents the volume of the solid obtained by revolving S about the y-axis. Do not evaluate the integral....
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## This note was uploaded on 05/01/2008 for the course MATH 125 taught by Professor Chen during the Spring '08 term at University of Washington.

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mid1f - R b a f y dy Do not evaluate the integral(s(c(4 pts...

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