Byronic Hero
Storyboard Text
- Hi! I just bought this property right next to yours, and I was wondering if you knew how big it is.
- Welcome neighbor! I don't know how big it is, but I may know a way to find out!
- Perfect, what did you have in mind?
- Well, the people who built our houses gave us the equation of the curve that makes up the top of the land, since it happens to look like an ln graph! Because we have this equation, we can estimate the area using a left Reimann sum approximation!
- That's right!
- Perfect! Should we use four subintervals?
- Sounds great! If this is the equation,: "1/4[f(-1)+f(-.75)+f(-.5)+f(-.25)]" then the land should be about 1.167 square miles in area, right!
- Thanks for your help with that part of the land, one more part left!
- What difference does that make?
- Sounds great! This time, we have two equations!
- Oh! That makes sense!
- Well, if you have two equations, then you can make a more accurate calculation by subtracting the bottom curve from the top curve to find the area between the curves, and then taking the integral!
- So our integral would be from 0 to 4 and our equation to integrate would be "x^(1/2) -x+2"
- Ok! Our first equation is "y=x^(1/2)" and our second is "y=x-2"
- Meaning the area of this plot of land would be 5.333 square miles!
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