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Question Number 145646 by physicstutes last updated on 06/Jul/21

$$\mathrm{Find}\mathrm{the}\mathrm{arc}\mathrm{lenght}\mathrm{of}\mathrm{the}\mathrm{function}{y}^2=\frac{x^3}{a}\mathrm{where}a\mathrm{is}\mathrm{a}\mathrm{constant}\mathrm{for}$$$$0⩽x⩽\frac{7a}{3}$$

Answered by Olaf_Thorendsen last updated on 06/Jul/21

$$y^2=\frac{x^3}{a}$$$$y=\frac{x^{3/2}}{\sqrt{a}}$$$$y^{\prime }=\frac{3\sqrt{x}}{2\sqrt{a}}$$$$\mathrm{L}={\int }_0^{\frac{7a}{3}}\sqrt{1+y^{\prime 2}}dx$$$$\mathrm{L}={\int }_0^{\frac{7a}{3}}\sqrt{1+\frac{9x}{4a}}dx$$$$\mathrm{L}=\frac{8a}{27}{\left[{(1+\frac{9x}{4a})}^{3/2}\right]}_0^{\frac{7a}{3}}$$$$\mathrm{L}=\frac{8a}{27}(\frac{25a}{4}-1)=\frac{2a}{27}(25a-4)$$

Commented by physicstutes last updated on 06/Jul/21

$$\mathrm{I}\mathrm{appreciate}$$

Commented by gsk2684 last updated on 07/Jul/21

$$givenexpressionissymmetric$$$$aboutxaxis.finalanseris2L.check$$$$itoncesir.$$

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