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Home Trigonometric Functions Integration by Parts Integration by Parts - 8 | |
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Problems
Evaluate the integrals in Problems 1-35. 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.
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Home Trigonometric Functions Integration by Parts Integration by Parts - 8 |