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polymath257 · April 27, 2018 at 8:53 pm

GrandizerII · (This post was last modified: April 28, 2018 at 1:42 am by GrandizerII.)

GrandizerII · (This post was last modified: April 28, 2018 at 9:36 am by GrandizerII.)

polymath257 · April 28, 2018 at 9:51 am

GrandizerII · (This post was last modified: April 28, 2018 at 11:37 pm by GrandizerII.)

polymath257 · April 29, 2018 at 9:00 am

GrandizerII · April 30, 2018 at 9:48 am

polymath257 · April 30, 2018 at 1:15 pm

GrandizerII · April 30, 2018 at 7:42 pm

polymath257 · April 30, 2018 at 8:09 pm

(April 30, 2018 at 7:42 pm)Grandizer Wrote:
(April 30, 2018 at 1:15 pm)polymath257 Wrote: A related integral is that of sqrt(1-x^2). But this one can be done by 'elementary' methods. No substitution.

Hint: interpret as an area.

The area of the upper semicircle? I can do the definite integral from -1 to 1 intuitively, but indefinite integral without substitution I will have to think about for a while. But first, need to go to work now. So later.

Yes, the indefinite integral. If you can do it from -1 to 1, you have part of the basic idea.

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