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Unformatted text preview: 1. Evaluate the integrals (a) Z 4 1 ( √ x1 x ) 2 dx (b) Z 4 x √ 9 + x 2 dx . 2. Compute the integral Z (2 sin(3 x )x 2 sec 2 x 3 ) dx . 3. Find the area bounded between the graph of the function f ( x ) = x 312 x and the straight line y =3 x . 4. The speed of a particle is v ( t ) = 80 t 330 t 2 meter/sec. What is the average speed of this particle over the interval of time [1 , 4]? 5. Find the critical points of the function f ( x ) = Z 2 x 33 x 2 (1 + sin x ) 2010 dx. 6. Find the derivative of the fuction F ( x ) = Z sin x x 3 (cos t ) 17 dt . 7. Compute the volume of the solid body generated by revolving the region enclosed between the graph of the function f ( x ) = 1x 2 and the xaxis about the straight line y = 4. 8. Suppose that f1 ( x ) is the inverse of a diﬀerentiable function and let G ( x ) = sin( f1 ( x )). If f ( π ) = 3 and f ( π ) = 7, ﬁnd G (3) and G (3)....
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 Winter '05
 staff
 Math, Derivative, real exam

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