Let f(x) be a function defined by $f(x)=\int_1^xx(x^2-3x+2)dx,\,1≤x≤3$. Then the range of f(x) is:
Answer & explanation
Correct answer: option 3
f'(x) = x(x - 1)(x - 2)
$f(2)=-\frac{1}{4}$ f(3) = 2 f(1) = 0
$f_{min}=min[f(1),f(2),f(3)]=-\frac{1}{4}\,∀\, x∈[1,3]$
$f_{max}=max[f(1),f(3)]=2\,∀\, x∈[1,3]$; Range = $[-\frac{1}{4},2]$