# Integration, limits, and curves

Note: x is used as a letter only not as a multiply sign

1. Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line x=6.

2. Find the arc length of the graph of the function y = x^(3/2) - 1 over the interval [0,4]

3. Integrate

∫ [(Pi / 2) / 0] x cos x dx

4. Integrate

∫ (cos^3) x (sin^2) x dx

5. Integrate

∫ ((1) / ((x^2) (25-x^2)^(1/2))) dx

6. Integrate

∫ (((3x^2)-7x-2) / ((x^3)-x)) dx

7. Integrate

∫ ((x-1) / ((x^3)+(x^2))) dx

8. Find the limit of the improper integral

∫ [∞/1] (x+2) e^(-x) dx if it exists

9. Find the arc length of the curve given in parametric form by

x= t^2, y= 2t, 0 ≤ t ≤ 2.

Â© BrainMass Inc. brainmass.com December 24, 2021, 6:07 pm ad1c9bdddfhttps://brainmass.com/math/integrals/integration-limits-curves-92448

#### Solution Preview

Please see the attached file.

Note: x is used as a letter only not as a multiply sign

1.Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line ...

#### Solution Summary

This provides examples of integration, limit of an improper integral, and arc length of a curve.