If the tangents to the graph of the function `y= f(x)` make angle `(pi)/(4)` and `(pi)/(3)` with the x- axis at the point `x=2` and `x=4` respectively, then the value of `int_(2)^(4) f'(x)f''(x) dx ` is-

If the tangent to the graph functin y = f (x) makes angles pi/4 and pi/3 with the x-axis at the point x =2 and x =4 respectively, the value of int _(2) ^(4) f ' (x) f''(x) dx :

If f(x)=x+sin x, then find the value of int_(pi)^(2 pi)f^(-1)(x)dx

The tangent to the graph of the function y=f(x) at the point with abscissae x=1, x=2, x=3 make angles pi/6,pi/3 and pi/4 respectively. The value of int_1^3f\'(x)f\'\'(x)dx+int_2^3f\'\'(x)dx is (A) (4-3sqrt(3))/3 (B) (4sqrt(3)-1)/(3sqrt(3)) (C) (4-3sqrt(3))/2 (D) (3sqrt(3)-1)/2

A line tangent to the graph of the function y=f(x) at the point x= a forms an angle (pi)/(3) with the axis of Abscissa and angle (pi)/(4) at the point x=b then int_(a)^(b)f'(x)dx is

A line tangent to the graph of the function y=f(x) at the pointx =a forms an angle pi/3 with y axis abd at x=b and pi/4 with x-axis then int_a^bf''(x)dx

What is the value of int_0^pi((f(x))/(f(x)+f(pi/2-x)))dx ?

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 pi/3 and at the point with abscissa x=b at an angle of pi/4 , then the value of the integral, int_1^b f'(x).f'' (x) dx is equal to

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 pi/3 and at the point with abscissa x=b at an angle of pi/4 , then the value of the integral, int_a^b f'(x).f'' (x) dx is equal to

If the normal to the curve y=f(x) at (1, 2) make an angle (3pi)/(4) with positive X-axis, then f'(1)=