Question

Let $f\,\,\left( x \right)$ be a function satisfying $f'\,\,\left( x \right) = f\left( x \right)$ with $f\left( 0 \right) = 1$ and $g\,\,\left( x \right)$ be a function that satisfies $f\,\,\left( x \right) + g\left( x \right) = {x^2}$. Then, the value of the integral $\mathop \smallint \limits_0^1 \,f\left( x \right)\;\,\,g\,\,\left( x \right)\;\,dx$, is

Accepted Answer

$e\,\, - \,\,\frac{{{e^2}}}{2}\,\, - \,\,\frac{3}{2}$

Answer

$e\,\, + \,\,\frac{{{e^2}}}{2}\,\, + \,\,\frac{5}{2}$

Answer

$e\,\, - \,\,\frac{{{e^2}}}{2}\,\, - \,\,\frac{5}{2}$

Answer

$e + \frac{{{e^2}}}{2}\,\, - \,\,\frac{3}{2}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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