Investigate for the maxima and minima of the function `f(x)=int_1^x[2(t-1)(t-2)^3+3(t-1)^2(t-2)^2]dt`

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

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

(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 m and n are positive integers and f(x) = int_1^x(t-a )^(2n) (t-b)^(2m+1) dt , a!=b , then

Find the interval of increase or decrease of the f(x)=int_(-1)^(x)(t^(2)+2t)(t^(2)-1)dt

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

If f(x)=t^(2)+(3)/(2)t , then f(q-1)=

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

Number of critical points of the function. f(x)=(2)/(3)sqrt(x^(3))-(x)/(2)+int_(1)^(x)((1)/(2)+(1)/(2)cos2t-sqrt(t)) dt which lie in the interval [-2pi,2pi] is………. .