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Definite Integration question

2024 · 30 Jan · Shift 2 · Q33

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PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 30 Jan · Shift 2 · Q33

Definite Integration question

2024 · 30 Jan · Shift 2 · Q33

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

y=f(x)

be a thrice differentiable function in

(-5,5)

. Let the tangents to the curve

y=f(x)

at

(1, f(1))

and

(3, f(3))

make angles

\pi / 6

and

\pi / 4

, respectively with positive

x

-axis. If

27 \int\limits_1^3\left(\left(f^{\prime}(t)\right)^2+1\right) f^{\prime \prime}(t) dt=\alpha+\beta \sqrt{3}

where

\alpha, \beta

are integers, then the value of

\alpha+\beta

equals

A
26
B
$-$ 16
C
36
D
$-$ 14

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