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Definite Integration question

2025 · 28 Jan · Shift 2 · Q28

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PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 28 Jan · Shift 2 · Q28

Definite Integration question

2025 · 28 Jan · Shift 2 · Q28

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}

be a twice differentiable function such that

f(2)=1

. If

\mathrm{F}(\mathrm{x})=\mathrm{x} f(\mathrm{x})

for all

\mathrm{x} \in \mathrm{R}

,

\int\limits_0^2 x F^{\prime}(x) d x=6

and

\int\limits_0^2 x^2 F^{\prime \prime}(x) d x=40

, then

F^{\prime}(2)+\int\limits_0^2 F(x) d x

is equal to :

A
13
B
11
C
9
D
15

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