# Area of a property using integration

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You own a plot of riverfront property which is pictured in the figure. Your property runs along the x-axis from x=0 to x=100 and is bounded by the lines x=0, x=100 and the River Sine.

1. What is the equation of the River Sine?

2. What is the area of the plot?

3. You have $600 to spend, and you hire a gardening firm to install a fence along the riverside part of your property. The firm will charge you $3 a foot for the fence including installation. If there is any money left over, the firm will fertilize the lot. They charge $20 a bag for fertilizer. One bag of fertilizer will cover 1,000 square feet.

a. Will there be any money left for fertilizer after the fence along the river is installed? Justify your response.

b. If there is money for fertilizer, about how much of your plot will be fertilizer? Justify your response.

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##### Solution Summary

This uses integration to find the area of a property. The equation of the River Sine is found.

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See attachment.

a)

b)

c)

This is unsolvable by methods learned by ...

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