# 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/