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

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.

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

Please see the attached file for the fully formatted problems.


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.