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

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

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)

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

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 4: If f(x) is a comtinuous function on [a;b] then int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

If int_0^(a) f(x ) dx = m and fx is an even and continuous function defined on [-a,a] , then evaluate int_(-a)^(a) f(x) dx (a in R^(+))

Prove that \int_{0}^(2a) f(x) dx = \int_{0}^a [f(x) + f(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