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Let $D$ be the region bounded below by the plane $z=0$, above by the sphere $x^{2}+y^{2}+z^{2}=4,$ and on the sides by the cylinder $x^{2}+y^{2}=1 .$ 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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a) $\int_{0}^{\sqrt{4-r^{2}}} r d z d r d f$b) $\int_{0}^{2 \pi} \int_{0}^{\sqrt{3}} \int_{0}^{1} x d x d z d \theta$ +$\int_{0}^{2 \pi} \int_{\sqrt{3}}^{2} \int_{0}^{\sqrt{4-z^{2}}} r d r d z d \theta$c) $\int_{0}^{1} \int_{0}^{\sqrt{4-r^{2}}} \int_{0}^{2 \pi} d \theta r d z d r$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

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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.

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Let $D$ be the region boun…

09:51

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$$\begin{array}{l}{\te…

09:43

05:07

Let D be the region bounde…

02:31

02:10

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