Math 230 Calculus IISummer 2004


7 problems, 10 points each


1. Show enough work to justify your answers

2. Don't use calculators for integration.

3. Don't leave until you are sure you've solved all the problems.

  1. Set up the Riemann sum for the area of the circle of radius $R$ as the area between two curves, provide an illustration and the integral formula. Evaluate for extra 5 points.

  2. The region bounded by the graphs of $y=x^{2}+1,y=0,x=0,$ and $x=1$ is revolved about the $x$-axis. Find the volume area of the solid generated.

  3. An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium (the density of water is 1000 kg/m$^{3})$.

  4. Evaluate the indefinite integral MATH

  5. Evaluate the indefinite integral MATH

  6. Find the partial fraction decomposition for the indefinite integral
    Do not evaluate the coefficients.

  7. Evaluate the indefinite integral MATH

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