# Fubini's Theorem

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[[Application|Gaussian Integral]]

## Example Question 1

This is the answer to the question, with a detailed solution. If math is needed, it can be done inline: \( x^2 = 144 \), or it can be in a centered display:

\[ \frac{x^2}{x+3} = 4y \]

And our final answer is 10. \( _\square \)

You are surveying a rectangular area of a bamboo forest of \(2 \times 3\) square feet. The four bamboos at the corners are each \(12, 27, 56, 59\) feet high, and when you analyze the surface area at the top, you find that it is a partial plain of \(f(x,y) = y^2 + x^3 - 2xy +7,\) as shown below.

Assuming the area is densely packed with bamboos, what is the average height of these bamboos in feet?

**Cite as:**Fubini's Theorem.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/fubinis-theorem/