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We are asked to use polar coordinates to find the volume under the paraboloid $z = x^2 + y^2$ and above the disk $x^2 + y^2 \leq 49$. Recall that as the paraboloid is given in the form $z = f(x, y)$, the volume below $f(x, y)$ and above the given disc is given by the following. $V = \iint_D f(x, y) dA = \iint_D (x^2 + y^2) dA$ To change the integral to polar coordinates, we must express the disc in polar coordinates, which is as follows. $D = \{(r, \theta) | 0 \leq r \leq \boxed{7}, 0 \leq \theta \leq \boxed{2\pi}\}$

Name: we are asked to use polar coordinates to find the volume under the paraboloid z x2 y2 and above the disk x2 y2 leq 49 recall that as the paraboloid is given in the form z fx y the volume bel 98856
Uploaded: 2023-08-05T22:31:28-08:00
Duration: 1 min 28 s
Channel: Zack A
Description: we are asked to use polar coordinates to find the volume under the paraboloid z x2 y2 and above the disk x2 y2 leq 49 recall that as the paraboloid is given in the form z fx y the volume bel 98856

          We are asked to use polar coordinates to find the volume under the paraboloid $z = x^2 + y^2$ and above the disk $x^2 + y^2 \leq 49$.
Recall that as the paraboloid is given in the form $z = f(x, y)$, the volume below $f(x, y)$ and above the given disc is given by the following.
$V = \iint_D f(x, y) dA = \iint_D (x^2 + y^2) dA$
To change the integral to polar coordinates, we must express the disc in polar coordinates, which is as follows.
$D = \{(r, \theta) | 0 \leq r \leq \boxed{7}, 0 \leq \theta \leq \boxed{2\pi}\}$

we are asked to use polar coordinates to find the volume under the paraboloid z x2 y2 and above the disk x2 y2 leq 49 recall that as the paraboloid is given in the form z fx y the volume bel 98856

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