# Thread: Comparison properties of integrals?

1. ## Comparison properties of integrals?

All right. Here's the problem.

Use this principle:
If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b-a) ≤ the integral ≤ M(b-a)

And here's my specific problem:

Use that property along with what you know about the function to estimate the value of

http://online2.byu.edu/webwork2_file...55353ba131.png

the answer should be in the form of "something" ≤ the integral ≤ "something"

Does that make sense? Help?

2. Originally Posted by lauren72
All right. Here's the problem.

Use this principle:
If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b-a) ≤ the integral ≤ M(b-a)

And here's my specific problem:

Use that property along with what you know about the function to estimate the value of

http://online2.byu.edu/webwork2_file...55353ba131.png

the answer should be in the form of "something" ≤ the integral ≤ "something"

Does that make sense? Help?
$f(x) = \cos{x}$

$a = \frac{\pi}{6}$ , b = $\frac{\pi}{4}$

$b-a = \frac{\pi}{12}$

$\frac{\sqrt{2}}{2} \le \cos{x} \le \frac{\sqrt{3}}{2}
$

$\frac{\pi\sqrt{2}}{24} \le \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \cos{x} \le \frac{\pi\sqrt{3}}{24}$