" (ii) "int_(0)^(a)(dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

Prove that : int_(0)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

Prove that (pi)/(6)

int_(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx=(pi-2)/(4)

Show that int_(0)^(1//3)(dx)/((1+x^(2))sqrt(1-x^(2))) = (pi)/(4sqrt(2))

The value of the expression (int_(0)^(a)x^(4)sqrt(a^(2)-x^(2))dx)/(int_(0)^(a)x^(2)sqrt(a^(2)-x^(2))dx)=

int_(0)^(2)x^(2)sqrt(4-x^(2))dx=

" (b) "int_(0)^(a)sqrt((a-x)/(a+x))dx=a((pi)/(2)-1)

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta

int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))=int_(0)^((pi)/(2))(dx)/(1+sqrt(cot x))=(pi)/(4)