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Question

If $ I_1 = \int_{0}^{\frac{\pi}{2}} x \cdot \sin x \, dx $ and $ I_2 = \int_{0}^{\frac{\pi}{2}} x \cdot \cos x \, dx $, then which one of the following is true?

$ I_1 = I_2 $

$ I_1 + I_2 = 0 $

$ I_1 = \frac{\pi}{2} \cdot I_2 $

$ I_1 + I_2 = \frac{\pi}{2} $

Solution

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