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vagabundo [1.1K]
3 years ago
12

Find the average value of f over the given rectangle. f(x, y) = 3x2y, r has vertices (−5, 0), (−5, 3), (5, 3), (5, 0). g

Mathematics
1 answer:
AlekseyPX3 years ago
6 0
\dfrac{\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_R\mathrm dx\,\mathrm dy}
\dfrac{\displaystyle\int_{y=0}^{y=3}\int_{x=-5}^{x=5}3x^2y\,\mathrm dx\,\mathrm dy}{\displaystyle\int_{y=0}^{y=3}\int_{x=-5}^{x=5}\mathrm dx\,\mathrm dy}
\displaystyle\frac1{10}\left(\int_{y=0}^{y=3}y\,\mathrm dy\right)\left(\int_{x=-5}^{x=5}x^2\,\mathrm dx\right)
\dfrac{75}2
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