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March 2nd, 2016, 06:18 PM   #1
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Exclamation Confusion over the Fundamental Theorem

So I've been looking at ways to rewrite arcsin, and I found this:

arcsin (x/a) + C = the integral of 1 over the square root of a^2 minus x^2 dx

This is correct

But when I try to graph the DERIVATIVE of arcsin (x/a), I expected it to be the same graph as 1 over the square root of a^2 minus x^2 dx, which is the same thing as above but without the integral. However, this does not work, instead the a^2 must be a 1 for them to be the same. Why is this?
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March 2nd, 2016, 06:39 PM   #2
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Are you graphing it correctly, or is your derivative incorrect?

${\mathrm d \over \mathrm d x}\arcsin {x \over a} = \frac1a {1 \over \sqrt{1- \left({x \over a}\right)^2}}$
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March 2nd, 2016, 06:45 PM   #3
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What value did you use for the constant, $a$? I used $a=3$, and graphed both the derivative of $\arcsin(x/3)$ and $\dfrac{1}{\sqrt{9-x^2}}$.

Note that I added 1 to the square root function, effectively shifting it up one unit so it could be seen ... without doing so, the two graphs were superimposed.
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Last edited by skipjack; March 3rd, 2016 at 01:01 AM.
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March 2nd, 2016, 08:48 PM   #4
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I see what I've done wrong, sorry guys, thanks for always offering help though!!
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