Question

let f(x) be a continuous function on the closed interval [1,4] if 5<=f(x)<=9 on this interval, then the value of definite integral from 4 to 1 f(x)dx cannot be: 12? 18? 27? 15? 21?

Answer 1

cannot be 12

Answer 2

why?

Answer 3

lowest is 15, highest is 27 inclusive

Answer 4

from 1 to 4 equates to a base of 3

Answer 5

3*5(lowest number) = 15
3*9(highest number) = 27

Answer 6

how does 1 to 4 equate to a base of 3?

Answer 7

4-1

Answer 8

what does it mean to find the base for the integral?

Answer 9

integral = area under curve = base * average height

Answer 10

base as in length against the x-axis

Answer 11

ohh that makes more sense now!

Answer 12

\[5\le f(x)\le 9\]

so

\[\int\limits_{1}^{4}5dx\le \int\limits_{1}^{4}f(x)dx\le \int\limits_{1}^{4}9dx\]

\[15\le \int\limits_{1}^{4}f(x)dx\le 27\]