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Tagged with solid-of-revolution real-analysis
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Generalization of why the area of a surface of revolution is not $2 \pi \int_{a}^{b} (y) dx$
Based on the posts Areas versus volumes of revolution: why does the area require approximation by a cone? and Why is surface area not simply..., approximating an ND quantity in an ND region using N-1D ...
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What is the maximum value of $H(r)=\frac{1}{3} \pi r^2\sqrt{l-r^2} $ when $l=7$?
What is the maximum value of $H(r)=\frac{1}{3} \pi r^2\sqrt{l-r^2} $ when $l=7$?
I've computed the minima using derivative method,but I'm not able to calculate the maxima under the given condition...
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Confusion About Bounds on a Volume of Revolution
I'm having a little bit of trouble understanding how to determine the bounds and manipulate the equations of a complex solid of rotation problem. Here's a prime example of where I struggle:
Taken ...
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Solid of Revolution About y=2
Find the volume of the solid of revolution bounded by $y=x^4$ and $y=1$ rotated about $y=2$.
Here's my attempt:
$\pi\displaystyle\int_{-1}^1(2-x^4)^2dx$
$\pi\displaystyle\int_{-1}^1(4-4x^4+x^8)dx$
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