Sketch Graphs: Struggling with Blue Highlighted Part

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Im meant to sketch these 2 graphs, but i can't seem to know what to do with the part highlighted in blue.

And I am think then I am meant to draw it for a few periods. But i can't continue because i don't know how to draw the part in blue?
 

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hi gomes! :wink:

for the left-hand graph, just draw a little "x" at the position (0, 1/2) :smile:

it's understood that only the point at the centre of the "x" is actually meant! :wink:

(and then repeat for a few periods, as you say)

(oh, i think some people draw a dot with a circle round it instead)
 
thanks! And how big should the circle be? If i where to do it that way?
 

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about the size you've done them :smile:

but your circles are so wonky, i think you should go for the crosses … they're easier to draw! :wink:
 
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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