JEE MATHEMATICS MCQ: TANGENTS & NORMALS

1 Hard

1 of 1

Application +4 | -1

The equation of a curve is

y=f(x)

. The tangents at

(1, f(1)),(2, f(2))

and

(3, f(3))

make angles

\frac{\pi}{6}, \frac{\pi}{3}

and

\frac{\pi}{4}

respectively with the positive direction of the

x

-axis. Then, the value of

\int\limits_{2}^3 f^{\prime}(x) f^{\prime \prime}(x) d x+\int\limits_{1}^3 f^{\prime \prime}(x) d x

is equal to

View answer and explanation

Correct option: A

-\frac{1}{\sqrt{3}}

Option A (

-\frac{1}{\sqrt{3}}

) is correct because it is the result of evaluating the definite integral using the given derivative values.

More Questions from TANGENTS & NORMALS

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a

y=x^3-a x

x^2 y=1-y

x y=1-y

C

y^3-3 x y+2=0

H

\mathrm{C}

x

V

C

y

y-e^{x y}+x=0

y = f\left( x \right)

x

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z