20b_03f_1e

# 20b_03f_1e - t 3 dt 2 Express the following as integrals DO...

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Math 20B First Midterm 50 points October 23, 2003 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One sheet of NOTES is allowed. You must show your work to receive credit. 1. (8 points each) Evaluate the following. For the definite integrals, write your answers as rational numbers. Remember to show your work! (a) Z xe 2 x dx . (b) Z 4 0 x 9 + x 2 dx . (c) Z 1 e x + 1 dx (d) Z 1 - 1 sin( t 3 ) dt . Hint : This is very simple when looked at the right way. (e) g 0 ( x ) where g ( x ) = Z 2003 x 2 sin(
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Unformatted text preview: t 3 ) dt . 2. Express the following as integrals. DO NOT EVALUATE the integals. Sketches may be useful in obtaining partial credit if you make a mistake. (a) (3 points) The average of the positive values of f ( x ) = 9-x 2 ; that is, the average over those x for which f ( x ) ≥ 0. (b) (7 points) The volume of the solid obtained by rotating the region that lies below y = x and above y = x 2 about the y-axis. END OF EXAM...
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