If f (x) is the anti-derivative of `tan^(-1) sqrt(x)` such that the curve y = f(x) passes through the point (0,2) then f(x) =

If f'(x)=x-1, the equation of a curve y=f(x) passing through the point (1,0) is given by

Let F(x) be the anti derivative of f(x)=3cos x-2sin x whose graph passes through the the point ((pi)/(2),1) then F(0) is equal to=-

If (1)/(f(x)) is a anti-derivative of log[f(x)]^(2)+c then f(x)=...

The slope of the tangent to a curve, y = f(x) at (x, f(x)) is 2x+1. If the curve passes through the point (1,2) , then the area of the region bounded by the curve, the x -axis and the line x=1

The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the curve passes through the point (1,2) then the area of the region bounded by the curve, the x-axis and the line x=1 is

If f(x) =tan ^(-1)x,then derivative of f(tan x) w.r.t. f(cot x) is

Let f:[0, oo)->R be a continuous function such that f(x)=1-2x+int_0^x e^(x-t)f(t)dt for all x in [0, oo) . Then, which of the following statement(s) is (are) TRUE? The curve y=f(x) passes through the point (1, 2) (b) The curve y=f(x) passes through the point (2, -1) (c) The area of the region {(x , y) in [0, 1]xxR :f(x)lt=ylt=sqrt(1-x^2)} is (pi-2)/4 (d) The area of the region {(x , y) in [0, 1]xxR :f(x)lt=ylt=sqrt(1-x^2)} is (pi-1)/4

The anti - derivative of f(x) = e^(x//2) whose graph passes through the point (0,3) is :