Show that `int0af(x)g(x)dx=2int0af(x)dx` if f and g defined as `f(x)" "=" "f(a-x)` and `g(x)" "+g(a-x)=" "4`

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

Evaluate: int[f(x)g''(x)-f''(x)g(x)]dx

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

Prove that int_a^bf(x)dx=int_(a+c)^(b+c)f(x-c)dx , and when f(x) is odd function, int_(-a)^af(x)dx=0

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

If the functions of f and g are defined by f(x)=3x-4 and g(x)=2+3x then g^(-1)(f^(-1)(5))

Let f(x)=f(a-x) and g(x)+g(a-x)=4 then int_0^af(x)g(x)dx is equal to (A) 2int_0^af(x)dx (B) int_0^af(x)dx (C) 4int_0^af(x)dx (D) 0

if int_(0)^f(x) 4x^(3)dx=g(x)(x-2) if f(2)=6 and f'(2)=(1)/(48) then find lim_(x to 2) g(x)

The integral int_(0)^(a) (g(x))/(f(x)+f(a-x))dx vanishes, if

Let f(x) and g(x) be differentiable functions such that f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+(g(x))^(2) = 1,"then" f(x) and g (x) respectively , can be