Tagged Questions
3
votes
1answer
358 views
Volume from revolving $e^x$ around $y$-axis
In school, I had a problem something like this:
A region R is bounded by $x$-axis, $y$-axis, $x = 3$, and $y = e^x$. What is the volume
of the solid produced by revolving it around the $y$-axis.
...
1
vote
1answer
94 views
Surface area of revolution about $y$-axis in terms of $f(x)$
I need to find a formula for the surface area of a solid of revolution rotated around the $y$-axis. The curve is $f(x)=x^2$ on $[0,1]$. However, my answer must be in terms of $f$, not $f^{-1}$.
2
votes
1answer
405 views
Volume of the torus with an integral
I am stuck on the following question:
Find the volume of the torus obtained by rotating the circle $(x-a)^2+y^2=b^2$, where $a>b$, around the y-axis.
2
votes
1answer
484 views
Solid of revolution about a slanted line
I just thought about this idea and I decided to work on it.
After taking on a general case, which proved to be too difficult, I tried a specific case. Something simple like the curve $y_1 = x^2$ ...
7
votes
2answers
599 views
Volume of a pyramid, using an integral
I have a calculus exam tomorrow and this is a possible question. However, I don't know how to handle this question.
Suppose you have 3 points in space: $p_1=(a,0,0)$, $p_2=(0,b,0)$ and $p_3=(0,0,c)$, ...
