JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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 the function satisfying

f\left( x \right)\,\, + \,\,g\left( x \right) = {x^2}

. The, value of the integral

\int \limits_0^1 \,f\left( x \right)\,\,g\,\,\left( x \right)dx

, is

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the calculated integral value does not match any of the provided options. The correct integral is

e - \frac{1}{2}{e^2} - \frac{3}{2}

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