If `int_(sinx)^(1)t^(2)f(t)dt=1-sinx,` where `x in(0,(pi)/(2))`, then find the value of `f((1)/(sqrt(3)))`.

Find the range of f(x)=(1)/(5sinx-6) .

If (sinx)/(siny)=(1)/(2),(cosx)/(cosy)=(3)/(2) , where x,y in (0,(pi)/(2)) , then the value of tan (x+y) is equal to

If int_(-1)^(4)f(x)dx=4" and "int_(2)^(4)(3-f(x))dx=7 , then find the value of int_(2)^(-1)f(x)dx is

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is

If f(x)=int_(1)^(x)(tan^(-1)(t))/(t)dt,AA x in R^(+) then the value of f(e^(2))-f((1)/(e^(2))) is a)0 b) pi/2 c) pi d) 2pi

find the derivative of f(x)=(x^2+1)sinx

If int_(0)^(x)f(t)dt=x+int_(x)^(1)tf(t)dt , then the value of f(1) is

If int_(0)^(x)f(x)sintdt= constant, 0ltxlt2pi and f(pi)=2 , then the value of f(pi//2) is a)3 b)2 c)4 d)8

Find the value of int_(0)^(1)3sqrt(2x^(3)-3x^(2)-x+1)dx .