" (i) "int_(0)^(a)(sqrt(x)dx)/(sqrt(x)+sqrt(a-x))

By using the properties of definte, prove that int_(0)^(a)(sqrt(x)dx)/(sqrt(x)+sqrt(a-x))=a/2

int_(0)^(a)(sqrtx)/(sqrt(x) + sqrt(a-x))dx .

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (a) int_(0)^(a) (sqrt(x))/(sqrt(x) + sqrt(a) - x)dx

int(dx)/(sqrt(x)sqrt(5-x))

int(dx)/(sqrt(x)sqrt(1-x))

2. int_(0)^(5)(sqrt(x))/(sqrt(x)+sqrt(5-x))dx

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

int_(0)^(1)x+sqrt(x)dx=