A line tangent to the graph of the function y -fx at the point x-a forms an angle -3 with the axis of abscissas and angle -4 at the point x-b then -abf-xdx is f- is assumed to be a continuous function

The correct option is D 1 √(3) f^1(a)=√(3) f^1(b)=1 ∫_a^bf^11(x)dx=f^1(x)∫_a^b =f^1(b) f^1(a) 1 √(3) ...

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Byju's Answer

Standard XII

Mathematics

Centre of Ellipse

A line tangen...

Question

A line tangent to the graph of the function $y = f (x)$ at the point $x = a$ forms an angle $π / 3$ with the axis of abscissas and angle $π / 4$ at the point $x = b$ then $\int_{a}^{b} f^{''} (x) d x$ is $(f^{''}$ is assumed to be a continuous function)

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1 - \sqrt{3}

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\sqrt{2} - 1

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\sqrt{3} - 1

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Solution

The correct option is D $1 - \sqrt{3}$
$f^{1} (a) = \sqrt{3}$
$f^{1} (b) = 1$
$\int_{a}^{b} f^{11} (x) d x = f^{1} (x) \int_{a}^{b}$
$= f^{1} (b) - f^{1} (a)$
$1 - \sqrt{3}$

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Similar questions

Q. A line tangent to the graph of the function

y = f (x)

at the point

x = a

forms an angle

π / 3

with

y

-axis and at

x = b

and angle

π / 4

with

x

-axis then

\int_{a}^{b} f^{''} (x) d x

Q. The tangent to the graph of the function y = f(x) at the point with abscissa x = a forms with the x-axis an angle of

\frac{π}{4}

and at the point with abscissa x = b at an angle of

\frac{π}{3}

, then find the value of

b \int a f^{'} (x) . f^{''} (x) d x

Q. The tangent to the graph of the function

y = f (x)

at the point with abscissa x = a forms with the x-axis an angle of

π / 3

and at the point with abscissa x = b at an angle of

π / 4

, then the value of the integral,

\int_{a}^{b} f^{'} (x) . f^{''} (x) d x

is equal to

Q. The tangent of the graph of the function y = f(x) at the point with abscissa x = 1 form an angle of

\frac{π}{6}

and at the point x = 2 an angle of

\frac{π}{3}

and at the point x = 3 angle of

\frac{π}{4}

. The value of

\int_{1}^{3} f^{'} (x) f " (x) d x + \int_{1}^{3} f " (x) d x (f " (x))

is suppose to be continuous) is

Q. The tangent to the curve

y = f (x)

at the point with abscissa

x = 1

form an angle of

\frac{π}{6}

and at the point

x = 2

an angle of

\frac{π}{3}

and at the point

x = 3

an angle of

\frac{π}{4}

. If

f^{n} (x)

is continuous, then the value of

\int_{1}^{3} f^{''} (x) f^{'} (x) d x + \int_{2}^{3} f^{''} (x) d x

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A line tangent to the graph of the function y=f(x) at the point x=a forms an angle π/3 with the axis of abscissas and angle π/4 at the point x=b then ∫baf′′(x)dx is (f′′ is assumed to be a continuous function)

The correct option is D 1−√3 f1(a)=√3f1(b)=1∫baf11(x)dx=f1(x)∫ba=f1(b)−f1(a)1−√3

A line tangent to the graph of the function $y = f (x)$ at the point $x = a$ forms an angle $π / 3$ with the axis of abscissas and angle $π / 4$ at the point $x = b$ then $\int_{a}^{b} f^{''} (x) d x$ is $(f^{''}$ is assumed to be a continuous function)

The correct option is D $1 - \sqrt{3}$
$f^{1} (a) = \sqrt{3}$
$f^{1} (b) = 1$
$\int_{a}^{b} f^{11} (x) d x = f^{1} (x) \int_{a}^{b}$
$= f^{1} (b) - f^{1} (a)$
$1 - \sqrt{3}$