Let `f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) ` for `x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1),` then:

Let f(x)=int_(x^(2))^(x^(3)) for x>1 and g(x)=int_(1)^(x)(2t^(2)-Int)f(t)dt(x<1) then

f (x) = int _(0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt 0) then :

f (x) = int _(0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt 0) then :

If F(x) =int_(x^(2))^(x^(3)) log t dt (x gt 0) , then F'(x) equals

If F(x) =int_(x^(2))^(x^(3)) log t dt (x gt 0) , then F'(x) equals

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)

Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = int_(1)^(x)((2(t-1))/(t+1)-lnt) f(t) dt for all x in (1,oo) . Which of the following is true ?

If F(x) = int_(x^(2))^(x^(3)) log t dt ,( t gt 0) then F^(')(x) is equal to

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then