Q. if `int_0^100(f(x) dx = a`, then `sum_(r=1)^100(int_0^1( f(r-1+x)dx))`=

If int_(0)^(100) f(x)dx=7, then sum_(r=1)^(100)int_(0)^(1)(r-1+x)dx= _________.

int_(0)^(2a) f(x) dx = 0 if ……… .

If f(x) is continuous for all real values of x , then sum_(r=1)^nint_0^1f(r-1+x)dx is equal to (a) int_0^nf(x)dx (b) int_0^1f(x)dx (c) int_0^1f(x)dx (d) (n-1)int_0^1f(x)dx

If int_(0)^(2a) f (x) dx = 2 int_(0)^(a) f(x) then

Find int_(0)^(1)(2x+3)dx as the limit of a sum

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 .

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=