g(x)=int_(sin x)^( sin2x)sin^(-1)(t)dt," then "

If g(x) =int_(sinx)^(sin2x) sin^(-1)(t) dt, then

g(x)=int_(sin(x))^(sin(2x))sin^(-1)(x)dx

phi(x)=int_(1/x)^( sqrt(x))sin(t^(2))dt, then find the value of phi'(1)

(i) If f(x) = int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t) dt, then prove that f'(x) = 0 AA x in R . (ii) Find the value of x for which function f(x) = int_(-1)^(x) t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum.

If f(x)=int_(0)^(x)(sin^(4)t+cos^(4)t)dt, then f(x+pi) will be equal to

If phi (x) =int_(1//x)^(sqrt(x)) sin(t^(2))dt then phi ' (1)is equal to

If phi(x) = int_(1//x)^(sqrtx) sin(t^2) dt, then phi'(1) is equal to