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Integration, limits, and curves

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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.

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

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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 ...

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