if f x int0 pow x log 1 t pow 2 dt then the value of f 1 is

If $$f\left( x \right) = \int_0^x {\log \left( {1 + {t^2}} \right)dt} $$ then the value of $$f''\left( 1 \right)$$ is equal to :

A. 2

B. 0

C. 1

D. none of these

Answer : 1

Solution :
$$\eqalign{ & f'\left( x \right) = \log \left( {1 + {x^2}} \right) \cr & \therefore f''\left( x \right) = \frac{{2x}}{{1 + {x^2}}} \cr & \therefore f''\left( 1 \right) = 1 \cr} $$

Releted MCQ Question on
Calculus >> Application of Integration

Releted Question 1

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

A. $$\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$

B. $$\sin \,\left( {3x + 4} \right)$$

C. $$\sin \,\left( {3x + 4} \right) + 3\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$

D. none of these

View Answer

Releted Question 2

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

A. $$1$$

B. $$2$$

C. $$2\sqrt 2 $$

D. $$4$$

View Answer

Releted Question 3

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

A. $$9$$

B. $$\frac{{27}}{4}$$

C. $$36$$

D. $$18$$

View Answer

Releted Question 4

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

A. $$\frac{1}{{\sqrt 3 }}$$

B. $$\frac{1}{2}$$

C. $$1$$

D. $$\frac{1}{3}$$

View Answer

If $$f\left( x \right) = \int_0^x {\log \left( {1 + {t^2}} \right)dt} $$ then the value of $$f''\left( 1 \right)$$ is equal to :

Releted MCQ Question on
Calculus >> Application of Integration

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

Practice More Releted MCQ Question on
Application of Integration

Practice More MCQ Question on Maths Section

If $$f\left( x \right) = \int_0^x {\log \left( {1 + {t^2}} \right)dt} $$ then the value of $$f''\left( 1 \right)$$ is equal to :

Releted MCQ Question on Calculus >> Application of Integration

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1st quadrant is-

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

Practice More Releted MCQ Question on Application of Integration

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Calculus >> Application of Integration

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

Practice More Releted MCQ Question on
Application of Integration