How do you find the volume of the region enclosed by the curves y=x, y=-x, and x=1 rotated about the y axis?

2 Answers
Oct 10, 2015

If rotating about the y-axis, the shell method is your best bet to a quick solution.

Explanation:

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Volume=2piint_0^1x[x-(-x)]dx=2piint_0^1(2x^2)dx

=4/3pi

hope that helped

Oct 10, 2015

Look at the big picture then break it apart into extrusions.

Explanation:

https://www.desmos.com/calculator/zem7gewjxm

I see it like a (Cylinder-2Cone) instead of a funky shape. So if we find the volume of the cylinder we get 2pi because pir^2h.

Now we have 2 Cones which are pir^2h/3 which turns out to be pi/3 because the height is now one. Now we take 2pi-2(pi/3) or a total V=(4pi)/3