`int_(-a)^(a)f(x)dx`

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

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

If f(a+x)=f(x), then prove that int_(a)^(na)f(x)dx=(n-1)int_(0)^(a)f(x)dx where a>0 and n in N.

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

If int_(0)^(a)f(x)dx=10 ,then Evaluate int_(0)^(a)f(a-x)dx

If int_(0)^(a)f(x)dx=10 ,then Evaluate int_(0)^(a)f(a-x)dx

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

Property 2: If the limits of a definite integral are interchanged then its value changes.int_(a)^(b)f(x)dx=-int_(b)^(a)f(x)dx

Property 3:int_(a)^(b)f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx

If |int_(a)^(b)f(x)dx|=int_(a)^(b)|f(x)|dx,a