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

(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_(-1)^(x)t(e^(t)-1)(t-1)(t-2)^(3)(t-3)^(5)dt has a local minimum then sum of values of x

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

The function f(x)=int_(-1)^x t(e^t-1)(t-1)(t-2)^3(t-3)^5dt has a local minimum at x= 0 (b) 1 (c) 2 (d) 3

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Let f(x) = int_(0)^(x)(t-1)(t-2)^(2) dt , then find a point of minimum.

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

The interval in which f(x)=int_(0)^(x){(t+1)(e^(t)-1)(t-2)(t-4)} dt increases and decreases

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then