Problem 86
Find the center of mass for \(\rho=\tan ^{2} x\) on \(x \in\left(-\frac{\pi}{4}, \frac{\pi}{4}\right)\).
Problem 88
The length of \(x\) for \(y=\cosh (x)\) from \(x=0\) to \(x=2\)
Problem 89
The length of \(y\) for \(x=3-\sqrt{y}\) from \(y=0\) to \(y=4\)
Problem 90
The shape created by revolving the region between \(y=4+x, y=3-x, x=0\), and \(x=2\) rotated around the \(y\) -axis.
Problem 91
The loudspeaker created by revolving \(y=1 / x\) from \(x=1\) to \(x=4\) around the \(x\) -axis.
Problem 93
You are a crime scene investigator attempting to determine the time of death of a victim. It is noon and \(45^{\circ} \mathrm{F}\) outside and the temperature of the body is \(78^{\circ} \mathrm{F}\). You know the cooling constant is \(k=0.00824^{\circ} \mathrm{F} / \mathrm{min} .\) When did the victim die, assuming that a human's temperature is \(98^{\circ} \mathrm{F}\) ?
Problem 96
Find surface area of the catenoid \(y=\cosh (x)\) from \(x=-1\) to \(x=1\) that is created by rotating this curve around the \(x\) -axis.
