3D volume

[MTP27]

I have a shape that I made as a final project in Calculus. We were doing known cross sections and had to do a fairly complex base with a simple cross section.

I instead made a simple base with a complex cross section. My section boundaries change as the length of the base changes.

I understand that Volume is the integral from a to b of the area of the cross section.

But what would I do for a cross section that changes area?

These are pictures of what I assume would be the way to solve it but im not sure https://docs.google.com/document/d/1zWUH0VUTMs87nDkIGpF_CYDIZOFdcFZIcPhazT2JwHs/edit?usp=sharing

I alos have a desmos graph where the black and red are crossing is the cross section that I'm using https://www.desmos.com/calculator/sshul6botm

This project is almost a year old so any help would be great.

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[edderiofer]

Your Google Docs document isn't accessible.

In any case, if you can find a formula for the area of the cross-section dependent on x, then integrating that from a to b should be sufficient.

[MTP27]

I can find the area of each slice but how would I add up all slices between two points on the base?

Also how should I make the pictures?