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Question

Mathematics Question on integral

Evaluate: ∫π4π2cos 2x dx\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x \,dx

A

14\frac{1}{4}

B

12\frac{1}{2}

C

−14-\frac{1}{4}

D

−12-\frac{1}{2}

Answer

−12-\frac{1}{2}

Explanation

Solution

We have, I=∫π4π2cos 2x dxI = \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x\,dx [sin 2x2]π4π2=−12\left[\frac{sin\,2x}{2}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}} = -\frac{1}{2}