Given that for each `a in (0,1) lim^(h to 0^(+)) int_(h)^(1-h) t^(-a)(1-t)^(a-1)dt` exists. If this limit be g(a), then the value `g((1)/(2))`, is

Given that for each a epsilon(0,1),lim(hto 0^(+)) int_(h)^(1-h)t^(-a)(1-t)^(a-1)dt exists. Let this limit be g(a) . In addition it is given the function g(a) is differentiable on (0,1) . The value of g(1/2) is

Given that for each a epsilon(0,1),lim(hto 0^(+)) int_(h)^(1-h)t^(-a)(1-t)^(a-1)dt exists. Let this limit be g(a) . In addition it is given the function g(a) is differentiable on (0,1) . The value of g(1/2) is a. (pi)/2 b. pi c. -(pi)/2 d. 0

Given that for each a epsilon(0,1),lim_(hto 0^(+)) int_(h)^(1-h)f^(-a)(1-t)^(a-1)dt exists. Let this limit be g(a) . In addition it is given the function g(a) is differentiable on (0,1) . The value of g(1/2) is

Given that for each a in(0,1) underset(hto0^(+))limint_(h)^(1-h)t^(-a)(1-t)^(a-1)dt exists. Let, this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1). The value of g'((1)/(2)) is

Given that for each a in(0,1) underset(hto0^(+))limint_(h)^(1-h)t^(-a)(1-t)^(a-1)dt exists. Let, this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1). The value of g((1)/(2)) is

Given that for each a in (0,1)lim_(x to 0) int_(h)^(-h) t^(-a)(1-t)^(a-1)dt exits and is equal to g(a).If g(a) is differentiable in (0,1), then the value of g'((1)/(2)) , is

int_(0)^(1)t^(5)*sqrt(1-t^(2))*dt

int_(0)^(1)t^(2)sqrt(1-t)*dt

The value of lim_(xto0)(1)/(x) int_(0)^(x)(1+ sin 2t)^(1/t) dt equals :