The equation of the curve is `y-f(x)`. The tangents at `[1,f(1)[,[2,f(2)]` and `[3,f(3)]` make angles `(pi)/6,(pi)/3` and `(pi)/4`, respectively with the positive direction of `x`-axis. Then the value of `int_(2)^(3)f'(x)f''(x)dx+int_(1)^(3)f''(x)dx` is equal to

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^('')dx+int_1^3f^('')dx is equal to -1/(sqrt(3)) (b) 1/(sqrt(3)) (e) 0 (d) none of these

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

If f(0)=0, f(3)=3 and f'(3)=4 , then the value of int_(0)^(1)xf'' (3x)dx is equal to

If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

If f((3x-4)/(3x+4))=x+2 , then int f(x)dx is equal to

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If fx=x+sinx , then int_(pi)^(2pi)f^(-1)(x)dx is equal to