"Convince yourself" of the lemma - is any work required?

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Homework Statement
In the homework statement part (a), it says to "convince yourself" of the given lemma. How do I satisfy this requirement for full credit?
Relevant Equations
Since I see these types of homework prompts often, does this mean that I should prove the given Lemma, or just accept it as true and move onto (b) with no work required by me?
Screen Shot 2021-11-06 at 3.35.39 PM.png
 
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'Convince yourself' means 'Prove'.
 
pasmith said:
'Convince yourself' means 'Prove'.
that explains why my homework grade was low 🥺
 
This is a terrible way to word a homework question.
 

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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