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Question Number 96604 by Rio Michael last updated on 03/Jun/20

$$\mathrm{Please}\mathrm{how}\mathrm{will}\mathrm{you}\mathrm{evaluate}$$$$\int \sqrt{dx}???$$

Commented by MJS last updated on 03/Jun/20

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{an}\mathrm{error}\mathrm{of}\mathrm{syntax}.‘‘{dx}^{″}\mathrm{has}\mathrm{to}\mathrm{be}\mathrm{the}\mathrm{last}$$$$\mathrm{term}\mathrm{of}\mathrm{an}\mathrm{integral}.‘‘{dx}^{″}\mathrm{can}\mathrm{never}\mathrm{be}\mathrm{a}$$$$\mathrm{part}\mathrm{of}\mathrm{the}\mathrm{term}\mathrm{you}\mathrm{want}\mathrm{to}\mathrm{integrate}.$$$$\int dx\mathrm{is}\mathrm{a}\mathrm{short}\mathrm{cut}\mathrm{for}\int 1dx;\int \frac{dx}{...}\mathrm{is}\mathrm{short}$$$$\mathrm{for}\int \frac{1}{...}dx$$$$\mathrm{but}$$$$\int \frac{...}{dx};\underset{dx}{\int }...;\int {dx}^n;\mathrm{generally}\int f\left(dx\right)\mathrm{are}\mathrm{all}$$$$\mathrm{meaningless}$$

Commented by prakash jain last updated on 03/Jun/20

Hi Rio, for fraction derivative study you can begin by reading wikipedia article https://en.m.wikipedia.org/wiki/Fractional_calculus

Commented by prakash jain last updated on 03/Jun/20

$$\frac{d^{1/2}}{{dx}^{1/2}}\sqrt{x}=\frac{\sqrt{\pi }}{2}$$$$\int \sqrt{dx}=\int d^{1/2}x=\frac{2}{\sqrt{\pi }}\sqrt{x}$$

Commented by MJS last updated on 03/Jun/20

$$\mathrm{I}\mathrm{know}\mathrm{about}\mathrm{fractional}\mathrm{derivates}\mathrm{and}$$$$\mathrm{integrals}\mathrm{but}\mathrm{I}\mathrm{think}\mathrm{most}\mathrm{of}\mathrm{these}\mathrm{questions}$$$$\mathrm{in}\mathrm{here}\mathrm{are}\mathrm{rather}\mathrm{typos}$$

Commented by Rio Michael last updated on 03/Jun/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}\mathrm{i}\mathrm{will}\mathrm{check}\mathrm{it}\mathrm{out}.$$

Commented by Rio Michael last updated on 03/Jun/20

$$\mathrm{Sir}\mathrm{i}\mathrm{think}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{just}\mathrm{some}\mathrm{way}\mathrm{to}\mathrm{solve}$$$$\mathrm{it},\mathrm{just}\mathrm{some}\mathrm{way}\mathrm{to}\mathrm{solve}\mathrm{it}..\mathrm{an}{\mathrm{i}}^{\prime }\mathrm{m}\mathrm{guessing}$$$$\mathrm{fractional}\mathrm{integral}\mathrm{should}\mathrm{work}.$$

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