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LuckyWell [14K]
3 years ago
6

Evaluate the double integral i=∫∫dxyda where d is the triangular region with vertices (0,0),(4,0),(0,4).

Mathematics
1 answer:
mario62 [17]3 years ago
8 0
I=\displaystyle\iint_D\mathrm dA=\int_{x=0}^{x=4}\int_{y=0}^{y=4-x}\mathrm dy\,\mathrm dx
I=\displaystyle\int_{x=0}^{x=4}(4-x)\,\mathrm dx
I=8

To verify this, we can simply find the area of the triangle using the well-known formula \dfrac12bh, where b and h are the base and height, respectively of the triangular region D. We have b=h=4, so the area is \dfrac{4^2}2=8, as expected.
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