Find the cylindrical coordinate for the Cartesian coordinate ( x , y , z ) = ( 1 , − 1 , 3 ) . \left(x,y,z\right)=\left(1,-1,\ 3\right). ( x , y , z ) = ( 1 , − 1 , 3 ) .

( 2 , − π 4 , 3 ) \left(\sqrt{2},-\frac{\pi}{4},3\right) ( 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , − 4 π , 3 )

( 2 , π 4 , 3 ) \left(\sqrt{2},\frac{\pi}{4},3\right) ( 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 4 π , 3 )

( 11 , π 4 , 3 ) \left(\sqrt{11},\frac{\pi}{4},3\right) ( 1 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 4 π , 3 )

( 11 , − π 4 , 3 ) \left(\sqrt{11},-\frac{\pi}{4},3\right) ( 1 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , − 4 π , 3 )

What is the concept of iterated integrals?

A mathematical concept used to calculate multiple integrals by breaking the region into smaller pieces and integrating over each piece.

A cooking technique used to prepare multiple dishes simultaneously

A concept in computer programming for repeating a sequence of instructions

A method for solving algebraic equations using repeated addition

How do you determine the limits of integration for a double integral?

Consider the region of integration and the bounds of the variables involved.

Use the value of the function at a single point

Ask someone else to determine the limits

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Authored by CALOS SALAS PEÑA

Mathematics

1st - 5th Grade

Used 2+ times

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61 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int\int\int\left(2x-3y+4z\right)dxdydz$

$xyz\left(x+\frac{3}{2}y+2z\right)+C$

$xyz\left(x-3y+2z\right)+C$

$xyz\left(x-\frac{3}{2}y+2z\right)+C$

$xyz\left(x+3y+2z\right)+C$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int\int\int\left(x^2+y^2+z^2\right)dxdydz$

$3xyz\left(x^2yz+xy^2z+xyz^2\right)+C$

$\frac{1}{3}xyz\left(x^2+y^2+z^2\right)+C$

$xyz\left(x^2yz+xy^2z+xyz^2\right)+C$

$\frac{1}{3}xyz\left(x^2y^2z+xy^2z^2+x^2yz^2\right)+C$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int\int\int e^{4x}dxdydz$

$\frac{1}{3}e^{4xy}yz+C$

$\frac{1}{3}e^{4x}yz+C$

$\frac{1}{4}e^{4x}xyz+C$

$\frac{1}{4}e^{4x}yz+C$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_0^1\int_1^2\int_3^4\ \left(-x-y-z\right)dxdydz$

5.50

-5.50

8.50

-8.50

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_2^4\int_6^8\int_{-2}^{-4}\ \cos\left(y\right)\ dxdydz$

$-8.05$

$\approx-0.192$

$\approx-2.19$

$\approx-5.08$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int_2^4\int_6^8\int_{-2}^{-4}\ \left(e^z\right)\ dxdydz$

$\approx-189$

$\approx-132$

$\approx538$

$\approx710$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the lower limit of z in the triple integral
$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$ if D is the solid bounded by $z=4-y,\ z=y-6$ and $y=x^2,$ taking the order of integration as $dzdydx$ .

$5$

$y-6$

$4-y$

$0$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the upper limit of z in the triple integral
$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$ if D is the solid bounded by $z=4-y,\ z=y-6\$ and $y=x^2,$ taking the order of integration as $dzdydx$ .

$5$

$y-6$

$4-y$

$0$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the upper limit of y in the triple integral
$\int_{ }^{ }\int_{ }^{ }\int_D^{ }\ \ f\left(x,y,z\right)dV$ if D is the solid bounded by $z=4-y,\ z=y-6$ and $y=x^2,$ taking the order of integration as $dzdydx$ .

$x^2$

$5$

$z+6$

$0$

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\int\int\int\left(2x-3y+4z\right)dxdydz$

$xyz\left(x+\frac{3}{2}y+2z\right)+C$

$xyz\left(x-3y+2z\right)+C$

$xyz\left(x-\frac{3}{2}y+2z\right)+C$

$xyz\left(x+3y+2z\right)+C$

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untitled

∫∫∫(2x−3y+4z)dxdydz\int\int\int\left(2x-3y+4z\right)dxdydz∫∫∫(2x−3y+4z)dxdydz

∫∫∫(x2+y2+z2)dxdydz\int\int\int\left(x^2+y^2+z^2\right)dxdydz∫∫∫(x2+y2+z2)dxdydz

∫∫∫e4xdxdydz\int\int\int e^{4x}dxdydz∫∫∫e4xdxdydz

∫01∫12∫34 (−x−y−z)dxdydz\int_0^1\int_1^2\int_3^4\ \left(-x-y-z\right)dxdydz∫01​∫12​∫34​ (−x−y−z)dxdydz

∫24∫68∫−2−4 cos⁡(y) dxdydz\int_2^4\int_6^8\int_{-2}^{-4}\ \cos\left(y\right)\ dxdydz∫24​∫68​∫−2−4​ cos(y) dxdydz

∫24∫68∫−2−4 (ez) dxdydz\int_2^4\int_6^8\int_{-2}^{-4}\ \left(e^z\right)\ dxdydz∫24​∫68​∫−2−4​ (ez) dxdydz

∫∫∫(2x−3y+4z)dxdydz\int\int\int\left(2x-3y+4z\right)dxdydz∫∫∫(2x−3y+4z)dxdydz

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$\int\int\int\left(2x-3y+4z\right)dxdydz$

$\int\int\int\left(x^2+y^2+z^2\right)dxdydz$

$\int\int\int e^{4x}dxdydz$

$\int_0^1\int_1^2\int_3^4\ \left(-x-y-z\right)dxdydz$

$\int_2^4\int_6^8\int_{-2}^{-4}\ \cos\left(y\right)\ dxdydz$

$\int_2^4\int_6^8\int_{-2}^{-4}\ \left(e^z\right)\ dxdydz$

$\int\int\int\left(2x-3y+4z\right)dxdydz$