10th - the given curve: (a) y = 3 + 2 x-x 2 , x + y = 3...

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Math 119 Recitation 10 November 21, 2006 1. Find the area of the region bounded by y 2 = 2 x and x - y = 4. 2. Let R be the region between the parabolas y = x 2 and y = 8 x . (a) Find the area of R . (b) Find the volume of the solid of revolution that we obtain when we rotate R about x -axis. (c) Find the volume of the solid of revolution that we obtain when we rotate R about y -axis. 3. Find the volume of the solid obtained by rotating about the y -axis the region bounded by the curves: (a) y = x 3 , y = 8, y -axis. (b) y = x 2 , x = 2, x -axis. 4. Find the volume of the solid obtained by rotating the region bounded by the curve y = x , y = 3, and x = 4 about the line x = 4. 5. The base of a certain solid is a circular disk with 2-inch radius. Cross sections perpendicular to the one of the diameters of the disk are square. Find the volume of the solid. 6. Find the volume of the solid obtained by rotating the given region around
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Unformatted text preview: the given curve: (a) y = 3 + 2 x-x 2 , x + y = 3 about y-axis. (b) x = 1 + y 2 , x = 0, y = 1, y = 2 about x-axis. 7. Show that if f and g are integrable on an interval [ a, b ], then R b a f 2 ( x ) dx + R b a g 2 ( x ) dx ≥ 2 R b a f ( x ) g ( x ) dx 8. Evaluate R π/ 3 π/ 6 [ D x (sin x )-2-( D x sin x )-2 ] dx . 9. Evaluate R 2 π ( | 2 cos x + 1 | + b 2 cos x + 1 c ) dx 1 10. Find the volume of the solid generated by rotating about the x-axis the region the first quadrant bounded by the y-axis and the sine and cosine curves. 11. Find the volume of the solid generated by rotating about the x-axis the region bounded by the curves y = x 3 , x = 2 and the x-axis. 2...
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10th - the given curve: (a) y = 3 + 2 x-x 2 , x + y = 3...

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