int_((x)/(2))^(x)sqrt(3-2sin^(2)x)*dx+int_(0)^((dy)/(dx)t*dt)

If int_((pi)/(3))^(x)sqrt((3-sin^(2)t))dt+int_(0)^(y)cos tdt=0, then evaluate (dy)/(dx)

Find the derivative (dy)/(dx) of the following implicit functions : (a) int_(0)^(y) e^(-t^(2)) dt + int_(0)^(x^(3)) sin ^(2) t dt = 0 (b) int_(0)^(y) e^(t) dt + int _(0)^(x) sin t dt = 0 (c) int _(pi//2)^(x) sqrt(3 - 2 sin^(2)z ) dz + int_(0)^(y) cos t dt = 0

If int_(pi//3)^(x)sqrt((3-sin^(2)t))dt+int_(0)^(y)cost dt =0 then (dy)/(dx) is

1) int_(-(pi)/(2))^(pi)sin^(-1)(sin x)dx 2) int_(-(pi)/(2))^((pi)/(2))(-(pi)/(2))/(sqrt(cos x sin^(2)x))dx 3) int_(0)^(2)2x[x]dx

int_(-a)^(a)x^(3)sqrt(a^(2)-x^(2))dx=0

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)=

If x=int_(0)^(y)sqrt(1+t^(2))dt, find (dy)/(dx)

If y = int_(0)^(x) (t^(2))/(sqrt(t^(2)+1))dt then (dy)/(dx) at x=1 is