The Radius Starts at the Axis

You'll learnto measure a radius from whatever line the region is being spun about, to get the order of subtraction from which side the region is on, to keep the cross term the shift creates, and to test the radius where it has to vanish.

Writing the radius as f(x) worked in Topic 8.9 for one reason: the line being spun about was y = 0. Move that line to y = 2 and the radius becomes the distance from it. One ten-second check catches every error here — work out the radius where the region touches the line, because it has to come out zero there. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · TEST THE RADIUS WHERE IT MUST VANISH · v2

A radius is the distance from whatever line the region spins about

Before you start

What you're looking at

A region and the dashed amber line it is being spun about, which this time is not a coordinate axis. Each radius is a segment starting on that line and ending on the boundary.

The question

How far is the boundary from that line here, and which way round does the subtraction go?

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