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)^(2a)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

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

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

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

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

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Prove that int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx . Hence find int_(0)^((pi)/(2)) sin^(2) xdx

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If int_(0)^(a//2)f(x)dx=p," then "int_(0)^(a)f(x)dx is equal to