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Unformatted text preview: 1. Evaluate the integrals (a) Z 4 1 ( x-1 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 3-12 x and the straight line y =-3 x . 4. The speed of a particle is v ( t ) = 80 t 3-30 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 3-3 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 ) = 1-x 2 and the x-axis about the straight line y = 4. 8. Suppose that f-1 ( x ) is the inverse of a dierentiable function and let G ( x ) = sin( f-1 ( x )). If f ( ) = 3 and f ( ) = 7, nd G (3) and G (3)....
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This note was uploaded on 01/27/2010 for the course MATH 2B taught by Professor Staff during the Winter '05 term at UC Irvine.
- Winter '05