# Derivatives and integrals

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1.R is the region that lies between the curve y = (1 /( x2 + 4x + 5) ) and the x-axis from x = -3 to x = -1. Find:

(a) the area of R,

(b) the volume of the solid generated by revolving R around the y-axis.

(c) the volume of the solid generated by revolving R round the x-axis.

2.Evaluate: ∫ sinh6 x cosh xdx.

3.Given f(x) = csch-1 (1 / x2), find f'(x).

4.Evaluate ∫ ( (log3 x) / 2x) dx.

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#### Solution Summary

This shows how to find the area of a region and volume of solids using calculus, as well as a given integration and derivative.

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