JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The tangent of the curve

y = f\left( x \right)

at the point with abscissa

x = 1

form an angle of

\pi /6

and at the point

x = 2

an angle of

\pi /3

and at the point

x = 3

an angle of

\pi /4

. If

f''\left( x \right)

is continuous, then the value of

\mathop {\int \,\,}\limits_1^3 f''\left( x \right)f'\left( x \right)\,\,dx + \mathop {\int \,}\limits_2^3 f''\left( x \right)\,\,dx

, is

View answer and explanation

Correct option: C

\frac{{4 - 3\,\,\sqrt 3 }}{3}

Option C is correct because the expression simplifies to

\frac{{4 - 3\,\,\sqrt 3 }}{3}

after evaluating the integrals using the given information about the derivatives.

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