Answer to Question #345850 in Calculus for Roy

Question

Is this statement true or false ? provide reason for your answer 

d/dx[ _x²∫(π/2) e^2cost dt ] = -2xe^{2(cosx^2)}

Answer 1

$$\displaystyle\int_{x}^{2}\dfrac{\pi}{2}e^{2\cos t}dt=-\displaystyle\int_{2}^{x}\dfrac{\pi}{2}e^{2\cos t}dt$$

$$\dfrac{d}{dx}(\displaystyle\int_{x}^{2}\dfrac{\pi}{2}e^{2\cos t}dt)=-\dfrac{d}{dx}(\displaystyle\int_{2}^{x}\dfrac{\pi}{2}e^{2\cos t}dt)$$

$$=-\dfrac{\pi}{2}e^{2\cos x}$$

The statement is false.