Property 5: If `f(x)` is a continuous function defined on `[0,a]` then `int_0 ^a f(x) dx = int_0^a f(a-x) dx`

Property 8: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=int_(0)^(a){f(x)+f(-x)}dx

Property 6: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

Property 10: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=2int_(0)^(a)f(x)dx if f(2a-x)=f(x) and 0 if f(2a-x)=-f(x)

Property 9: If f(x) is a continuous function defined on [-a;a] then int_(-a)^(a)f(x)dx=0 if f(x) is odd and 2int_(0)^(a)f(x)dx if f(x) is even

If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove that int_0^(2a)f(x)dx=int_0^a{f(x)+(2a-x)}dx

Property 7: Let f(x) be a continuous function of x defined on [0;a] such that f(a-x)=f(x) then int_(0)^(a)xf(x)dx=(a)/(2)int_(0)^(a)f(x)dx

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

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

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

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx