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Question Number 186048 by ARUNG_Brandon_MBU last updated on 31/Jan/23

$${\int }_a^b\frac{dx}{\sqrt{b-x}+\sqrt{x-a}}$$

Commented by ARUNG_Brandon_MBU last updated on 31/Jan/23

$$\ne 0$$

Commented by MJS_new last updated on 31/Jan/23

$$\mathrm{sorry}{\mathrm{I}}^{\prime }\mathrm{ve}\mathrm{not}\mathrm{got}\mathrm{enough}\mathrm{time}\mathrm{right}\mathrm{now}$$$$\underset{a}{\stackrel{b}{\int }}...=2\underset{a}{\stackrel{(a+b)/2}{\int }}...$$$$\mathrm{solve}\mathrm{in}2\mathrm{steps}:$$$$t=\sqrt{b-x}+\sqrt{x-a}$$$$u=\arcsin \frac{\sqrt{2}t}{2\sqrt{b-a}}$$$$\mathrm{I}\mathrm{get}$$$$2\sqrt{b-a}+\sqrt{2(b-a)}\ln (-1+\sqrt{2})$$

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