Find-the-arc-lenght-of-the-function-y-2-x-3-a-where-a-is-a-constant-for-0-x-7a-3-

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

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

0 ⩽ x ⩽ \frac{7 a}{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^{'} = \frac{3 \sqrt{x}}{2 \sqrt{a}}

L = \int_{0}^{\frac{7 a}{3}} \sqrt{1 + y^{' 2}} d x

L = \int_{0}^{\frac{7 a}{3}} \sqrt{1 + \frac{9 x}{4 a}} d x

L = \frac{8 a}{27} {[{(1 + \frac{9 x}{4 a})}^{3 / 2}]}_{0}^{\frac{7 a}{3}}

L = \frac{8 a}{27} (\frac{25 a}{4} - 1) = \frac{2 a}{27} (25 a - 4)

Commented by physicstutes last updated on 06/Jul/21

I appreciate

Commented by gsk2684 last updated on 07/Jul/21

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a b o u t x a x i s . f i n a l a n s e r i s 2 L . c h e c k

i t o n c e s i r .

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