If f(x) is a continuous function that achieves a maximum value of 5 and a minimum value of -2 on the interval between x=1 and x=3, then, for F=∫f(x) dx, possible values of F are
a. -4

Question

If f(x) is a continuous function that achieves a maximum value of 5 and a minimum value of -2 on the interval between x=1 and x=3, then, for F=∫f(x) dx, possible values of F are 
a. -4<F<10 
b. -6<F<15 
c. -14<F<14 
d. -4<F<6 
e. none of these

anonymous · Answer

If it were -2 on the whole interval...the area of that region would be
2 * -2 = -4
If it were 5 on the whole interval...the area of that region would be
2 * 5 = 10

anonymous · Answer

So all I needed to do was solve for area, since that's the possible function y-values?

anonymous · Answer

yes...that's right.

anonymous · Answer

ugh.... and here i was thinking i needed to do actual calculus. thanks!