Trig substitution (integration)

joess
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Homework Statement


30x75o8.gif


Homework Equations



The Attempt at a Solution


I'm not asking for someone to do the question for me but I was just wondering what I'm supposed to sub in. Do I put in
2pyuz2w.gif
as if it was (x^2-9)^(1/2) or do I have to do something differently if there is a constant in front of the x^2? Thanks for any help.
 
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You are correct, secant is the correct trig function to use in this case.
However the coefficient is incomplete, you need to divide out the 4 as well.
 
So is it x=(3/2)sec(theta) ?
 
That's right! :)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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