HP preferred integration bug?

Integration attempt in trying to get the volume of a torus of revoling circle around the axis y.

Central circle of distance from the origin R and radius r using slices. Standard simple calc problem often given to students. Works well on HP50 and TI-89. Tried on first, last firmware using the template quite definite integral printing.

Integrate r - r-R + r.

Using equation 4 * pi * x * sqrt (r ^ 2-(x - R) ^ 2) dx

You should get 2 * pi ^ 2 * r ^ 2 * R.

First lets you: "impossible to verify if the antiderivative gibberish characters (rA ^ 2 x 3A gibberish talor has singular points for final integration in [-r, r]).

Thanks for coming back.

I just tested with several versions back, and each of them works fine. Make sure that R is not used (because it is an approximate numeric value).

∫ (4 * π * x * √ (R²-(x - R2) ²), x, R2 - r, R2 + r)-> 4 * π * r² * r2 * asin ((r/ABS (r)))

assume(R2>0), assume(r>0)-> [r r2]

∫ (4 * π * x * √ (R²-(x - R2) ²), x, R2 - r, R2 + r)-> 2 * π2 * r² * r2

I think the problem that I saw before was that I had swapped order of r2/r giving r - r2 and r2 + r instead. I think you've done the same too - take a look at your line of "4 * pi * x * sqrt (y ^ 2-(x - r) ^ 2), dx, r - y, r + y;   It works very well if you put r - y and y + r.

Tags: HP Tablets

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