Let `f` be a one-to-one continuous function such that `f(2)=3a n df(5)=7.G i v e nint_2^5f(x)dx=17 ,` then find the value of `int_3^7f^(-1)(x)dx`

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)dx

Let f: RvecR be a one-one onto differentiable function, such that f(2)=1a n df^(prime)(2)=3. The find the value of ((d/(dx)(f^(-1)(x))))_(x=1)

Let T >0 be a fixed real number. Suppose f is continuous function such that for all x in R ,f(x+T)=f(x)dot If I=int_0^Tf(x)dx , then the value of int_3^(3+3T)f(2x)dx is (a) 3/2I (b) 2I (c) 3I (d) 6I

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)