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

If int_(cosx)^1(t^2f(t)dt=1-cosx AA x in (0,pi/2) , then the value of [f((sqrt(3))/4)] is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) -7

Find the value of int (dx)/(1-2sinx) ​

f(x)=int_1^x(tan^(-1)(t))/t dt , x in R^+, then find the value of f(e^2)-f(1/(e^2))

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

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

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

Solve sinx >-1/2or find the domain of f(x)=1/(sqrt(1+2sinx))

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

If int_(0)^(x) f(t)dt=x^2+int_(x)^(1) t^2f(t)dt , then f'(1/2) is