fa07hw5 - 15. The volume remaining is b V = 2 a xh 1 - x2...

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Unformatted text preview: 15. The volume remaining is b V = 2 a xh 1 - x2 x3 - 2 3b x b b a dx = 2 h a3 2 = h(b2 - a 2 ) - h b2 - 3 b 3 1 2a = h b2 - 3a 2 + cu. units. 3 b y h x y b + h =1 x=a x dx b x Fig. 1-15 6. Rotate about a) the x-axis 1 V = 0 (x 2 - x 4 ) d x 1 1 1 = x3 - x5 3 5 b) the y-axis 1 = 0 2 cu. units. 15 V = 2 0 x(x - x 2 ) d x 1 1 1 = 2 x 3 - x 4 3 4 y = 0 cu. units. 6 (1,1) y=x y=x 2 x Fig. 1-6 4. Slicing: 1 V = 0 (y - y 4 ) dy 1 1 1 = y2 - y5 2 5 Shells: V = 2 0 1 = 0 3 cu. units. 10 x(x 1/2 - x 2 ) d x 1 2 1 = 2 x 5/2 - x 4 5 4 y = 0 3 cu. units. 10 (1,1) y= x y=x 2 x Fig. 1-4 1. By slicing: 1 V = 0 x4 dx = cu. units. 5 By shells: 1 V = 2 0 y(1 - y) dy 1 = 2 y2 2y 5/2 - 2 5 y y=x 2 = 0 cu. units. 5 (1,1) x x Fig. 1-1 ...
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