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Evaluate the definite integral ∫₀^(π) |cos x|³ dx.

1. 0
2. 4/3
3. 2/3
4. −4/3

Correct answer: 4/3

Solution

By symmetry of |cos x|, integral_0^pi |cos x|^3 dx = 2 integral_0^(pi/2) cos^3 x dx = 2*(2/3) = 4/3.

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