# 1 sketch the region bounded by the given curves then

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1. Sketch the region bounded by the given curves. Then use a definite integral to find its area.
2. Use the disk/washer method to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and a typical disk/washer.
3. Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and a typical shell. a) y = 1 /x , y = 0, x = 1, x = 2, about y -axis b) y = x , y = 0, x = 4, about y = 3
4. Evaluate each integral.
5. Evaluate each improper integral. a) integraldisplay 1 sin(1 /x ) x 2 dx b) integraldisplay 1 0 2 x dx c) integraldisplay 0 xe x dx 6. Find a family of solutions for the differential equation y + y 2 sin( x ) = 0. 7. Solve the initial value problem y x = x 2 + 1 y 2 , y ( 3) = 3. Your answer should give y as a function of x . 8.
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