JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

f(x)

be a function satisfying

f^{\prime}(x)=f(x)

with

f(0)=1

and

g

be the function satisfying

f(x)+g(x)=x^2

.

The value of the integral

\int_0^1 f(x) g(x) d x

View answer and explanation

Correct option: D

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

Option D is correct because by finding f(x) and g(x), we can evaluate the integral

\int_0^1 f(x) g(x) d x

which results in

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

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