The numbers of possible continuous `f(x)` defined in `[0,1]` for which `I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2 is//are` 1 (b) `oo` (c) 2 (d) 0

int_(0)^(a)f(x)dx=int_(a)^(0)f(a-x)dx .

int_(0)^(2a)f(x)dx=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx .

Evaluate int_0^1e^(2x) dx

int_0^5f(x) dx=.........'

int_0^oo 1/(1+x^2)dx is equal to :

int_0^1 (dx)/(1+x^2) is equal to :

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 3/2I (b) 2I (c) 3I (d) 6I

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(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2), then