# Thread: A simple integral and a tricky volume problem

1. ## A simple integral and a tricky volume problem

Coffee is draining from a full conical filter basket into a cylindrical coffee pot at the rate of 10in^3/min. How fast is the level in the pot rising when the height of the coffee in the filter is 5 inches? How fast is the level in the filter cone falling?

6"
----------- -
\ / |
\ / |
\------/<<<<<<< how fast does it fall?
\ / 5"
\ / |
\ / |
-

___________
| |
| |
| |
|-------------|<<<<<< How fast is this level rising?
| |
|__________|

<---6"------->

I am also stumped on another question which is probably easy for one of you the question is

Evaluate

the integral from -1 to 1 (sinx)/(1+x^2)dx <x in the denominator is being raised to the second power not everything sorry i do not know a better way of inputting this.

I was wondering if someone may be able to solve this rather quickly, i have NO Clue what so ever to even begin doing this, this was an extra assignment that was given to us today and due tomorrow 7-28-09. Please answer asap, thank you very much for your help on the last problem and thank you in advance.

P.S. i am sorry for posting in the wrong section, these questions come from my calc class.

2. the int from -a to a of an odd function is 0

an odd function is one in which f(-x) = -f(x)

sin(x)/(1+x^2) is odd since sin(-x)/[1+(-x)^2] = -sin(x)/(1+x^2)

therefore the int is 0