The function ` f(x) = int_-2015^x t (e^t-e^2) (e^t-1) (t+2014)^2015 (t-2015)^2016 (t-2016)^2017 ` dt has

In (-4,4) the function f(x)=int_(-10)^x (t^2-4)e^(-4t) dt , has

If f(x) = int_(0)^(x) t.e^(t) dt then f'(-1)=

In(-4,4) the function f(x)=int_(-10)^(x)(t^(4)-4)e^(-4t)dt has

(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.

Then function f(x)=int_(-2)^(x)t(e^(t)-1)(t-2)^(3)(t-3)^(5)dt has a local minima at x=

The function int_(-1)^(x)t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has local minimum at x=

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