(i) सिद्ध करे कि ` int _(0)^(t) f(x)" g "(t-x) dx = int _(0)^(t) g(x) f(t-x) dx `

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

Prove that int_0^t f(x)g(t-x)dx=int_0^t g(x)f(t-x)dx

If k int_(0)^(1) x f (3 x) dx = int_(0)^(3) t f(t) dt then k=

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then minimum value of f (x) is:

If k int _(0)^(1)x.f(3x)dx = int_(0)^(3) t. f(t)dt , then the value of k is

I=int_(0)^(T)f(x)dx, then show that int_(3)^(3+3T)f(2x)dx=3I