Find the length of the curve below from the the pointP = (1, 2) to the point Q = (8, 5).x² = (y – 1)³-

The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

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Find the length of the curve below from the the point
P = (1, 2) to the point Q = (8, 5).
x² = (y – 1)³
-

Expert Solution

Step 1

The length of arc for curve $y = f (x)$ from $x = a to x = b$ is given as follows.

$L = \int_{a}^{b} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x$

The given curve is $x^{2} = {(y - 1)}^{3}$ .

$x^{2} = {(y - 1)}^{3} x^{\frac{2}{3}} = y - 1 y = x^{\frac{2}{3}} + 1 \frac{d y}{d x} = \frac{2}{3} x^{- \frac{1}{3}}$

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Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y – 1)³