Question

The slope of the tangent to the curve $y={\int }_0^x\frac{dx}{1+x^3}$ at the point where $x=1$ is

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. None of these

Answer 1

The correct option is B $\frac{1}{2}$

Given, $y={\int }_0^x\frac{dx}{1+x^3}$

$\therefore \frac{dy}{dx}=\frac{1}{1+x^3}$

$\frac{dy}{dx}{|}_{x=1}=\frac{1}{1+x^3}{|}_{x=1}=\frac{1}{2}$