$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$

question 23

Multiple Choice

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
- $\mathrm { D }$ is the solid right cylinder whose base is the region in the xy-plane that lies inside the cardioid $r = 6 - 2$ sin $\theta$ and outside the circle $r = 4$ , and whose top lies in the plane $z = 10$ .

• A) \(\int_{0}^{\pi} \int_{4}^{6-2 \sin \theta} \int_{0}^{10} \mathrm{f}(\mathrm{r}, \theta, \mathrm{z}) \mathrm{dz} \mathrm{rdr} \mathrm{d} \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 4 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } \mathrm { f } ( \mathrm { r } , \theta , z ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } f ( r , \theta , z ) d z r d r d \theta\)
• D) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta\)

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Definitions:

Treppe

A phenomenon in muscle physiology where successive contractions become increasingly more forceful after several stimuli, often referred to as the "staircase effect."

Wave Summation

The phenomenon where muscle contractions become stronger due to the frequency of stimulation without allowing the muscle to fully relax between successive stimuli.

Treppe

A phenomenon observed in cardiac muscle, where successive stimuli result in increasingly stronger contractions, described as the "staircase effect."

Wave Summation

A phenomenon in muscle physiology where repeated stimulation of a muscle fiber leads to an increase in the strength of muscle contraction.