Question

$\int x f(x) dx + \frac{f(x)}{2} = 0$, then $f(x)$ is equal to

• A. $e^{-2x}$
• B. $e^{2x}$
• C. $e^{-x^2}$
• D. $e^{x^2}$

Hint:

Whenever you see an equation containing an integral of an unknown function (an integral equation), the standard first step is almost always to differentiate the entire equation with respect to the variable. This converts it into a manageable differential equation.

Answer 1

The Correct Option is C