Question

Set up iterated integrals to find the area of the region bounded by the graphs of 2-3y=0, x+y=5, and y=0. Write one integral for each order of integration. dy dx and dx dy

Answer 1

, I like to draw a picture for integrals, I hope it helps. Using the picture I was able to see that x epsilon [0,5.666666] and y epsilon [0,-.666666]. (the greek letter epsilon means "is a member of"). Furthermore, we know y=5-x and y=-2/3 so the dydx integral is \[\int\limits_{0}^{5.6666666}\int\limits_{-2/3}^{5-x} 2-3y dydx\] I did this rather quickly so there could be errors.