Show that : `int_(1)^(2)sqrt((x-1)(2-x))dx=(pi)/(8)`.

int_(2)^(5)sqrt((x-2)(5-x))dx=(9pi)/(8)

Show that int_(0)^(1)(cos^(-1)x)^(2)dx=pi-2 .

int_(1)^(sqrt3)(dx)/(1+x^(2))

int(x^(2)+1)/(sqrt(1-x^(2)))dx

Evaluate: int1/((x^2)sqrt(1-x^2))dx

Prove that, int_(2)^(3)(dx)/((x-1)sqrt(x^(2)-2x))=(pi)/(3)

Putting x=alphacos^(2)theta+betasin^(2)theta show that, int_(alpha)^(beta)sqrt((x-alpha)(beta-x))dx=((beta-alpha)^(2)pi)/(8)

int (x^(2)dx)/(sqrt(x+1))

Evaluate: int(dx)/(sqrt((x-1)(2-x))) by the substitution x=1+sin^(2)theta . Hence, find the value of int_(1)^(2)(dx)/(sqrt((x-1)(2-x)))

Evaluate: int1/((x+1)sqrt(x^2-1))dx