JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f(x)

be a function satisfying

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

with

f(0)=1

and

g(x)

be a function which satisfies

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

. Then

\int\limits_{0}^1 f(x) g(x) d x=

View answer and explanation

Correct option: D

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

Option D (

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

) is correct because it is the result of integrating the product of f(x) and g(x) from 0 to 1, where f(x) = e^x and g(x) = x² - e^x.

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