[" Green that for each "a in(0,1)" ,lim "int_(1)^(-oo)t^(-2)(1-t)^(2-1)dt" exists.Let this limit be "g(a)" .In addition,it "],[" is given that the function "g(t)" is differentiable on "(0,1).],[" (2) The ralue 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 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)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 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

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

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 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

Let g(x) be differentiable on R and int_( sin t)^(1)x^(2)g(x)dx=(1-sin t), where t in(0,(pi)/(2)). Then the value of g((1)/(sqrt(2))) is