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Question Number 168556 by mokys last updated on 13/Apr/22

$$\int \sqrt{sinx}dx$$

Answered by MJS_new last updated on 13/Apr/22

$$\mathrm{this}\mathrm{question}\mathrm{keeps}\mathrm{reappearing};{\mathrm{I}}^{\prime }\mathrm{ve}\mathrm{given}$$$$\mathrm{the}\mathrm{answer}\mathrm{before}...$$$$\int \sqrt{\sin x}dx=\int \sqrt{1-{\sin }^2\frac{2x-\pi }{4}}dx=$$$$[t=\frac{2x-\pi }{4}\to dx=2dt]$$$$=2\int \sqrt{1-{\sin }^{2}t}dt=2\mathrm{E}(t\mid 2)=$$$$=2\mathrm{E}(\frac{2x-\pi }{4}\mid 2)+C$$

Commented by peter frank last updated on 14/Apr/22

$$\mathrm{thanks}$$

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