Answer:
[tex]\displaystyle \int_{0}^{5}\int_{0}^{-3x+15}f(x,y) \ dy dx[/tex]
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Explanation:
We're tasked to find the values of a,b,c,d in the following
[tex]\displaystyle \int_{a}^{b}\int_{c}^{d}f(x,y) \ dy dx[/tex]
The equation of the line through the points (0,15) and (5,0) is y = -3x+15
When picking a particular fixed x value, the y values span from y = 0 to y = -3x+15 which determines the bounds of integration for the inner integral.
So this means c = 0 and d = -3x+15
The values of a,b are much easier and they are a = 0 and b = 5 to represent the x coordinates of the left-most and right-most points.
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Since,
- a = 0
- b = 5
- c = 0
- d = -3x+15
we go from this
[tex]\displaystyle \int_{a}^{b}\int_{c}^{d}f(x,y) \ dy dx[/tex]
to this
[tex]\displaystyle \int_{0}^{5}\int_{0}^{-3x+15}f(x,y) \ dy dx[/tex]
Without knowing what f(x,y) is, we cannot compute the integral. Luckily it seems like your teacher is only interested in setting up the integral rather than computing its numeric value.
