The value of the integral ∫−π$$/3$$π$$/3$$ xsin⁡$$xcos2$$⁡xdx is

Correct option is 222π3−log⁡(2+3)

Questions

The value of the integral $\int_{- π / 3}^{π / 3} \frac{x \sin x}{\cos^{2} x} d x$ is

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π3−log⁡tan⁡3π2

22π3−log⁡(2+3)

3π2−log⁡tan⁡π12

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detailed solution

Correct option is B

The integrand is an even function, so the given integral is equal to2∫0π/3 xsin⁡xcos2⁡xdx=2[xsec⁡x]0π−∫0π/3 sec⁡xdx=2⋅π3⋅2−2[log⁡(sec⁡x+tan⁡x)]05=4π3−2log⁡(2+3)

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The value of the integral ∫−π/3π/3 xsin⁡xcos2⁡xdx is

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The value of the integral $\int_{- π / 3}^{π / 3} \frac{x \sin x}{\cos^{2} x} d x$ is