The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Problems

Evaluate the integrals in Problems 1-35.

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36            Find the volume of the solid of revolution generated by rotating the region under the curve y = sin x, 0 ≤ x ≤ π, about (a) the x-axis, (b) the y-axis.

37            Prove that if f is a differentiable function of x, then

∫f(x)dx = x f(x)- ∫ x f'(x)dx.

38            If u and v are differentiable functions of x, show that

∫ f(x) dx = u2v - 2 ∫ uv du.

39            Show that if f' and g are differentiable for all x, then

∫ g(x) g'(x) f"(g(x))dx = f'(g(x))g(x) - f(g(x)) + C.


Last Update: 2006-11-25