Question

The value of $\frac{d}{dx}\underset{2}{\overset{x^2}{\int }}(t-1)dt$

• A. $(x^2-1)$
• B. $x(x^2-1)$
• C. $2x(x^2-1)$
• D. none of these

Answer 1

The correct option is C $2x(x^2-1)$

Given,

$\frac{d}{dx}\underset{2}{\overset{x^2}{\int }}(t-1)dt$.

Now applying the rule of differentiation under integral sign we get,

$\frac{d}{dx}\underset{2}{\overset{x^2}{\int }}(t-1)dt=(x^2-1).2x-(2-1).0=2x(x^2-1).$