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  4. Evaluate: ∫ limits(π/4)(π/2) cos 2x dx

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Q. Evaluate: $\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x \,dx $

Integrals

Solution:

We have, $I = \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x\,dx$
$\left[\frac{sin\,2x}{2}\right]_{\frac{\pi}{4}}^{\frac{\pi}{2}} = -\frac{1}{2} $