Integrals...(4)

Calculus Level 4

Let y ( x ) = π 2 16 x 2 cos ( x ) cos ( θ ) 1 + sin 2 ( θ ) d θ y(x)=\int_{\frac{\pi^2}{16}}^{x^2}\frac{\cos(x) \cos(\sqrt{\theta})}{1+\sin^2(\sqrt{\theta})}d\theta

Value of d y d x \frac{dy}{dx} at x = π x=\pi can be expressed as n π n\pi find find 4 n + 1 4n+1


The answer is 9.

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1 solution

Tanishq Varshney
Jul 11, 2015

Apply Newton Leibnitz first theorem. Substitute x= pi.

Answer is 2 π 2\pi

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