JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

y=f(x)

be a thrice differentiable function in

(-5,5).

Let the tangents to the curve

y=f(x)

(1, f(1))

and

(3, f(3))

make angles

\frac{\pi}{6}

and

\frac{\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) d t=\alpha+\beta \sqrt{3},

where

\alpha, \beta

are integers, then the value of

\alpha+\beta

equal

View answer and explanation

Correct option: D

26

The correct answer is D (26) because by using substitution and integration, we can find the values of alpha and beta and then calculate their sum.

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