If `f(2a-x)=-f(x)`, then show that, `int_(0)^(2a)f(x)dx=0`

If f(x)=f(a+x) then show that int_(0)^(2a)f(x)dx=2int_(0)^(a)f(x)dx .

Evaluate:If f(a-x)=f(x), then show that int_0^axf(x)dx=a/2int_0^af(x)dx

if f(x)=3x^(2)+4,0<=x<=2 and f(x)=9x-2,2<=x<=4 then show that int_(0)^(4)f(x)dx=66

If f and g are continuous functions on [0,a] satisfying f(x)=(a-x) and g(x)+g(a-x)=2 , then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx .

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions f(x)=f(a-x) and g(x)+g(a-x)=a , then show that int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx . Hence find the value of int_(0)^(pi)xsinxdx .

If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

If f(2a-x)=-f(x) then int_(0)^(2a)f(x)dx is equal to-

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If fandg are continuous function on [0,a] satisfying f(x)=f(a-x)andg(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx