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# 12 Problems - Integrals : Sum of Partial Fractions and Volume of Solid of Revolution

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36)After t weeks, contributions in response to a local fund raising campaign were coming in at a rate of 2000te^-0.2t dollars/week. How much money was raised during the first five weeks.

38) Find the volume of the solid generated when the region under the curve y=sinx+cosx on the interval [0,pi/4] is revolved about the y axis.

42) Solve the diff eq. Dy/dx = xe^y-x.
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7.4

Write each as a sum of partial fractions.

2) 3x-1/x^2-1

4) 2x^2 +5x-1/[x(x-1)]

8) x^2-5x-4/[(x^2+1)(x-3)]

12) x^4-x^2+2/[x^2(x-1)]

Compute the integrals. In each the integrand is a rational function decomposed into partial fractions

18) integral 2x^2+5x-1/[x(x^2-1)] dx

20) integral x^2-x+3/[x^2(x-1)] dx

Find the integrals

26) integral x^3 + 1/ x^3-1 dx

30) integral x+2/x(x-1)^2 dx

34) integral 5xdx/ x^2 -6x+9

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#### Solution Summary

Twelve problems involving integrals, sum of partial fractions and volume of solid of revolution are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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