Find the derivative of the following with respect to x.
(i) `int_(0)^(x) cos t dt`
(ii) `int_(0)^(x^(2)) cos^(2) dt`

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

Find the derivatives of the following functions : (a) F (x) = int_(1)^(x) " In t dt " (x gt 0) (b) F (x) = int_(2//x)^(x^(2)) (dt)/(t)

Lt_(x to oo) ((int_(0)^(x) e^(t) dt)^(2))/(int_(0)^(x)e^(2t^(2))dt)

Find the derivative with respect to x of the following functions : (a) F(x) = int_(0)^(2x) (sin t)/(t) dt , (b) f(x) = int_(x)^(0) sqrt(1 + t^(4)) dt

Find the derivative with respect to x of the following functions : (a) F(x) = int_(x^(2))^(x^(3)) "In t dt " (x gt 0) (b) f(x) = int_(1//x)^(sqrt(x)) cos (t^(2)) dt (x gt 0)

lim_( x to 0) ( int_(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

Find the derivative of F (x) = int _(pi//2) ^(x ^(3)) cos t dt

int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x) cos^(-1) sqrt(t) dt=