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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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- Spring '10