let f be a function defined on the closed interval [0,2]. If 2 <f(x)< 4 , then the greatest possible value of the integral from 0 to 2 f (x) dx

Question

Is the answer 4 or 8? 

Answer 1

Hi Ab,

 

I think the answer would be 8.  

 

Integration is the area under the curve, f(x).

 

If you let f(x) = 4, then integrate between x = 0 and x = 2, you would get a rectangle of area = 8