- #1
Hannisch
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- 0
Homework Statement
The problem, from the very beginning, was:
[tex]\int \sqrt{9-x^{2}}dx[/tex]
But this I have reduced to:
[tex]\int \sqrt{9-x^{2}}dx = \frac{x}{2} \sqrt{9-x^{2}} + \frac{9}{2} \int \frac{1}{\sqrt{9-x^{2}}}dx [/tex]
My problem is that last integral - I get a factor of (1/3) times the correct answer and I don't know what to do - I simply can't see it.
Homework Equations
[tex]\int \frac{1}{\sqrt{1-x^{2}}}dx = arcsinx[/tex]
The Attempt at a Solution
I look at it and want to "transform" my expression into something like the arcsin expression above. So I say:
[tex]\int \frac{1}{\sqrt{9-x^{2}}}dx = \int \frac{1}{3\sqrt{1-\frac{x^{2}}{9}}}dx[/tex]
and from there get:
[tex]\int \frac{1}{\sqrt{9-x^{2}}}dx = \frac{1}{3}arcsin\frac{x}{3}[/tex]
but you're not supposed to get that factor of 1/3 - you're not supposed to remove it? Can anyone explain to me what I'm missing? I've searched my textbook so many times now I'm about to throw it into the wall or something..