Evaluate the integral ∫_0^{π/2} sin^3(x) dx.
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Get StartedEvaluate the integral ∫_0^{π/2} sin^3(x) dx.
Options:
- 1/2
- 2/3
- 3/4
- π/4
Correct answer: 2/3
Explanation: Use sin^3 x = sin x(1−cos^2 x) and u=cos x, or Beta function; the definite integral equals 2/3, a standard result for odd powers of sine on [0,π/2].
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