21b_ps_final

21b_ps_final - 21B Final Review Pro blems 3 2 x 6x 2x 3 dx...

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21B Final Review Problems 1) x 3 + 6 x 2 + 2 x + 3 x 2 + 6 x + 1 dx ! " # 2) x + 1 x 4 + x 2 dx ! " # 3) ln(2 x ) x 2 dx ! " # 4) 1 x 3 + 1 dx ! " # 5) x 3 4 ! x 2 dx " # $ 6) dx x 4 x 2 ! 9 " # $ 7) Converge or diverge? a) x x 4 + 1 0 ! " # $ dx b) 2 + cos x x ! " # $ % dx c) 1 x ln x 1 e ! " # dx 8) Let R be the region under the first “arch” of y = sin x and above the x -axis from 0, [ ] . a) Find the volume of the solid formed by revolving R about the x -axis. b) Findthe volume of the solid formed by revolving R about the y -axis. c) SET UP an integral for the volume when R is revolved about the line x = 2 . 9) SET UP an integral for the area bounded by the graphs of x = y 2 and x = y + 6 . 10) Find the centroid of the region bounded by y = x 4 and y = 1 . Assume constant density. 11) A vertical dam 4 ft tall is in the shape of an isosceles trapezoid with the top of the dam 10 ft across and the bottom 4 ft across. SET UP an integral for the total force on the dam at full capacity. ( water
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This note was uploaded on 05/26/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at Berkeley.

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