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Area Under the Curves question

2025 · 4 Apr · Shift 1 · Q35

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PYQ Library
JEE Main
Mathematics
Area Under the Curves
2025 · 4 Apr · Shift 1 · Q35

Area Under the Curves question

2025 · 4 Apr · Shift 1 · Q35

JEE MainMathematicsArea Under the CurvesMCQ+4 / −1

Let

f:[0, \infty) \rightarrow \mathbb{R}

be a differentiable function such that

f(x)=1-2 x+\int_0^x e^{x-t} f(t) d t

for all

x \in[0, \infty)

. Then the area of the region bounded by

y=f(x)

and the coordinate axes is

A
$\sqrt5$
B
2
C
$\sqrt2$
D
$\frac{1}{2}$

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