Question

Find the maximum M and minimum m values of the given integrand on the interval shown. Then use the corresponding property of integrals to find upper and lower bounds (estimates) for the value of the integral.
http://i49.tinypic.com/33oijqh.jpg

Answer 1

derivative of the integrand is \(\frac{9-x^2}{(x^2+9)^2}\) has max at the zero of the derivative, namely at \(x=3\)

Answer 2

if you evaluate the integrand at \(x=3\) you get \(\frac{1}{6}\) and that is the max of the function on your interval

Answer 3

i think the min on that interval is at \(x=1\) which gives \(\frac{1}{10}\)

Answer 4

i tried that already

Answer 5

so the integral is bounded on the left by \(\frac{4}{10}=\frac{2}{5}\) and on the right by \(\frac{4}{6}=\frac{2}{3}\)

Answer 6

did you remember to multiply the max and min by the length of the path?

Answer 7

I thought I did, hold on

Answer 8

you gotta multiply the max and min by 4

Answer 9

I guess I didn't :P thanks -_-

Answer 10

whew all that work, and you forget to multiply !!

Answer 11

I know right?! UGH!

Answer 12

:) thanks again