Mathematics: Will give the answer brainliest.

Will give the answer brainliest. - id11115369, Brad876

Ответ:

arthkk0877

11.02.2021

Mathematics

less then

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Ответ:

matthesml

18.12.2021

Mathematics

$\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy$

Converting to cylindrical coordinates, the integral is equivalent to

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta$
$=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)$
$=\dfrac{2\times7^3}3=\dfrac{686}3$

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by

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Will give the answer brainliest.

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