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Let $D$ be the region bounded below by the cone $z=\sqrt{x^{2}+y^{2}}$ and above by the paraboloid $z=2-x^{2}-y^{2} .$ Set up the triple integrals in cylindrical coordinates that give the volume of $D$ using the following orders of integration. a. $d z d r d \theta$b. $d r d z d \theta$c. $d \theta d z d r$

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$\int_{0}^{1} \int_{r}^{2-r^{2}} \int_{0}^{2 \pi} r d \theta d z d r$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Johns Hopkins University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

04:18

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

26:18

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

02:19

$$\begin{array}{l}{\te…

09:43

Let $D$ be the region boun…

02:31

05:57

02:10

11:22

02:28

09:09

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