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

By using the properties of definte, prove that int_(0)^(pi//2)(sqrt(cotx))/(sqrt(tanx)+sqrt(cotx))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+sqrt(cotx))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)cos^(2)x dx=(pi)/4

By using the properties of definte, prove that int_(0)^(a)1/(x+sqrt(a^(2)-x^(2)))=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sinx)/(sinx+cosx)=(pi)/4

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3)x)/(sin^(3)x+cos^(3)x)dx=(pi)/4

By using the properties of definte, prove that int_(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx=(pi)/2

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

Using properties of definite integral prove that int_0^2 xsqrt(2-x)dx= (16sqrt2)/15