Property 6: If f(x) is a continuous function defined on `[0, 2a]` then ` int_0 ^(2a)f(x)dx = int_0 ^a f(x) dx + int_0 ^a f(2a - 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 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

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

int_0^a 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 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)

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

If int_(0)^(2a) f(x)dx=int_(0)^(2a) f(x)dx , then

If : int_(0)^(2a)f(x)dx=2.int_(0)^(a)f(x)dx , then :

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