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Give the limits of integration for evaluating the integral $$\iiint f(r, \theta, z) d z r d r d \theta$$ as an iterated integral over the region that is bounded below by the plane $z=0,$ on the side by the cylinder $r=\cos \theta,$ and on top by the paraboloid $z=3 r^{2}$

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$z=0 \quad>0=3 r^{2} \Rightarrow r=0$$r=0 \quad \rightarrow 0=\cos \theta-\cos ^{\prime} 0=\pm \frac{\pi}{2}$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

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.

02:38

Set up the iterated integr…

02:21

02:03

Give the limits of integra…

03:35

04:37

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