## Autograph: Area between 2 curves rotated about a line

In 2D: draw **y = x² – 4** and ** y = x(3 – x)**.

Use Point mode, with CTRL, to locate and mark the two points of intersection.

Use the Text Box to label them (you will need the x-coordinates in the 3D page)

Double-click on ‘A’ and associate it with **y = x(3 – x)**

Double-click on ‘B’ and associate it with **y = x² – 4**

Select ‘A’ and ‘B’ (in that order), and use right-click option” Find Area”

Use Simpsons’s Rule, which gives an exact answer for quadratics (and cubics)

In 3D: draw **y = x² – 4** and ** y = x(3 – x)**, using the option “plot as 2D”.

Select the top graph then the bottom graph, and right-click “Find Area”.

Enter left and right x-limits from 2D (-0.8508 and 2.351) and Simpson’s Rule

Draw** x = -1** (again with ‘plot as 2D’ selected)

With ‘Slow Plot’ on, select the area and the line and ‘Find Volume’

Download 2D Autograph File and 3D Autograph file (.agg). Watch Jing video!

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