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Unformatted text preview: the given curve: (a) y = 3 + 2 xx 2 , x + y = 3 about yaxis. (b) x = 1 + y 2 , x = 0, y = 1, y = 2 about xaxis. 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 xaxis the region the ﬁrst quadrant bounded by the yaxis and the sine and cosine curves. 11. Find the volume of the solid generated by rotating about the xaxis the region bounded by the curves y = x 3 , x = 2 and the xaxis. 2...
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 Spring '10
 Tor
 Math, Cartesian Coordinate System, Region, Euclidean geometry

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