- #1

Lo.Lee.Ta.

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**Find the volume between y=-2x + 4, x-axis, x=1, about the line x=1. Check my work? :)**

Hi, everyone.

1. Find the volume of the region between y= -2x + 4, x-axis, x=1, about the line x=1.

I tried to post this before, but I don't think it went through!

2. Alright, so I first drew it out, and the shape is a cone.

Since it revolves around a y-axis, the limits should be also in terms of y.

Every cross-section is a circle.

So this is how I wrote it out:

∫0 to 4 of ∏[((-y/2) + 1)^2]dy

∫0 to 4 of ∏[(y^2/4) -y + 1]

= 1/4 * (y^3)/3) - (y^2)/2) + x |0 to 4

= ((y^3)/12) - 1/2(y^2) + x |0 to 4

= ((4)^3)/3 - 1/2(4)^2 + 4 -(0)

= 64/12 - 8 + 4

= 1.33 or 4/3

So... Is that right?

Thank you so much for checking my work! :)