2 years ago

If you were to take a cross section of a right circular cone parallel to its base, what shape would you get?

Mathematics

1 answer:

Mademuasel [1]2 years ago

6 0

Answer:

Step-by-step explanation:

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

mario62 [17]

$I=\displaystyle\iint_D\mathrm dA=\int_{x=0}^{x=4}\int_{y=0}^{y=4-x}\mathrm dy\,\mathrm dx$
$I=\displaystyle\int_{x=0}^{x=4}(4-x)\,\mathrm dx$
$I=8$

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.