Math 182 Miniproject 4 The Volume of a Football.md
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Math 182 Miniproject 4 The Volume of a Football
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**Overview:** In this project we find exact formulas for integral approximations using Riemann sums of various flavors.

**Prerequisites:** Section 6.2 of _Active Calculus_.

Go to https://www.desmos.com/calculator/c7aip1g33m to see a regulation size football image. (All units are inches.)

1. Using your graph plotting kung fu, find a curve that approximates the boundary of (at least part of) the football.

$y = \frac{-1}{12}x^2 + 3.3$

2. Set up an integral expression that will give the volume of the football.

$\int\pi(-\frac{1}{12}x^2 + 3.3)^2 dx$
The bound of integration would be from -5.5 to 5.6

3. Use Desmos to find the value of your integral. What is the volume of the football?

For my volume i got 85.2321940901 $cm^2$ but the way I had my curve this is a slight overestimation.

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