How do you find the arc length of the curve $y = 2 - x^{2}$ $y = 2 − x^2$ from [0,1]?

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Answer 1 · 2015-09-09T11:04:50

It is given by the integral $L = \int_{0}^{1} \sqrt{1 + {(\frac{d y}{d x})}^{2}} d x$ $L=int_0^1sqrt(1+(dy/dx)^2)dx$

Hence $\frac{d y}{d x} = - 2 x$ $dy/dx=-2x$ we have that

$L = \int_{0}^{1} \sqrt{1 + 4 x^{2}} d x$ $L=int_0^1sqrt(1+4x^2)dx$

For the calculation of the integral see below

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How do you find the arc length of the curve y = 2 − x^2y=2−x2y = 2 − x^2 from [0,1]?