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Definite Integration question

2024 · 4 Apr · Shift 2 · Q37

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PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 4 Apr · Shift 2 · Q37

Definite Integration question

2024 · 4 Apr · Shift 2 · Q37

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f(x)=\int_0^x\left(t+\sin \left(1-e^t\right)\right) d t, x \in \mathbb{R}

. Then,

\lim_{x \rightarrow 0} \frac{f(x)}{x^3}

is equal to

A
$\frac{1}{6}$
B
$-\frac{1}{6}$
C
$\frac{2}{3}$
D
$-\frac{2}{3}$

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