Calculate RMS Voltage & Fourier Coefficients for 10Ω Load & 240V 50Hz

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A single-phase ac voltage regulator has a resistive load of R= 10 ohms, and the input voltage is Vs = 240 V, 50 Hz. The delay angle of each of the Thyristors is ɑ = Π/2. Determine:

(a) The rms value of the output voltage.
(b) The Fourier coefficients of the fundamental, 11th and 13th current harmonics
 
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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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