Bacteria is growing on a slide which corresponds to [0,20] ×[ 0,5] , where distances are in centimeters. If the density of the bacteria is determined to be
f( x,y) = 1000xy( 20-x) ( 5-y) bacteria

cm2
then about how many bacteria are on the slide?

Question

Bacteria is growing on a slide which corresponds to [0,20] ×[ 0,5] , where distances are in centimeters. If the density of the bacteria is determined to be
f( x,y) = 1000xy( 20-x) ( 5-y)   	  bacteria

cm2
then about how many bacteria are on the slide?

anteater · Answer

Number of bacteria should be density times area, so $$\int\limits_{0}^{20}\int\limits_{0}^{5}1000xy(20-x)(5-y)dydx$$ should give the number of bacteria.

anteater · Answer

(or you could do the integral in the other order as well ala Fubini)

anonymous · Answer

thanks mate

anteater · Answer

Welcome :)