arc-length-3x-3-2-1-from-x-0-and-x-1-help-please-sir-

Question Number 95653 by rb222 last updated on 26/May/20

a r c l e n g t h 3 x^{\frac{3}{2}} - 1

f r o m x = 0 a n d x = 1

h e l p p l e a s e s i r

Answered by john santu last updated on 26/May/20

Arc L = \underset{0}{\int^{1}} \sqrt{1 + {(\frac{dy}{dx})}^{2}} dx

\frac{dy}{dx} = \frac{9}{2} \sqrt{x}

\underset{0}{\int^{1}} \sqrt{1 + \frac{81 x}{4}} dx = \frac{1}{2} \underset{0}{\int^{1}} \sqrt{4 + 81 x} dx

= \frac{1}{2} {[\frac{{(4 + 81 x)}^{3 / 2}}{\frac{243}{2}}]}_{0}^{1}

= \frac{85 \sqrt{85} - 8}{243}

Answered by MAB last updated on 26/May/20

d l = \sqrt{{(d x)}^{2} + {(d y)}^{2}}

d l = \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x

l = \int_{0}^{1} \sqrt{1 + {(f^{'} (x))}^{2}} d x

l = \int_{0}^{1} \sqrt{1 + \frac{81}{4} x} d x

l = {[\frac{8}{243} {(1 + \frac{81}{4} x)}^{\frac{3}{2}}]}_{0}^{1}

l = \frac{85 \sqrt{85} - 8}{243}

Commented by rb222 last updated on 27/May/20

t h a n k s s i r

Commented by MAB last updated on 06/Jun/20

y o u a r e w e l c o m e

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