Question

Let f(x) be a continuous function on the closed interval [1,4]. If 5<_ f(x) <_9, then the least possible value for integral from 1 to 4 of f(x)dx is?

Answer 1

Where's my @wio?

Answer 2

hmm

Answer 3

Well, the lowest it could be is for \(f(x)=5\), no?

Answer 4

So why not try: \[
\int_1^4 5 dx
\]

Answer 5

Never forget that an integral is just a sum: \[
\lim_{\Delta x\to 0}\sum_i f(x_i)\Delta x
\]The larger the function value on the interval, the larger the sum on the interval.