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
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 72809. 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.