NIELIT 2016 MAR Scientist B - Section B: 11

Question

What is the derivative w.r.t $x$ of the function given by

$\large \Phi(x)= \displaystyle \int_{0}^{x^2}\sqrt t\:dt$,

• A. $2x^2$
• B. $\sqrt x$
• C. $0$
• D. $1$

Answer 1

Integrating the function first and then applying limits, we get:

$\Phi (x)=\frac{2}{3}\left [ (x^{2})^{1.5}-0 \right ]$  $=$  $\frac{2}{3}x^{3}$

$\frac{d}{dx}(\frac{2}{3}x^{3})=2x^{2}$

Option A is correct.

Answer 2

Apply Newton Leibniz rule