`int_(-a)^af(x)dx=int_0^a[f(x)+f(-x)]dx`

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

int_(0)^(a)f(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 is an integrable function, show that int_(-a)^af(x^2)dx=2int_0^af(x^2)dx

Prove that : int_(-a)^(a)f(x)dx =2 int_(a)^(0) f(x)dx, if f(x) is even funtion =0 , if f(x) is off fuction.

Prove the following properties of definite integrals : int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

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

int_(-a)^(a)f(x)dx= 2int_(0)^(a)f(x)dx, if f is an even function 0, if f is an odd function.

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

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