Find the length of the arc of the semi cubical parabola y2=x2 between the points (1,1) and (4,8)

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Suresh Chand · Accepted Answer

Solution Given parabola is y2 = x2 Then (Rightarrow 2y frac{dy}{dx} = 2x) (Rightarrow left ( frac{dy}{dx} right )^2 = left ( frac{x}{y} right )^2 = 1) (Rightarrow 1 + left ( frac{dy}{dx} right )^2 = 2) Now the arc length of the arc of y2 = x2 from (1, 1) to (4, 8) is Arc Length = (int_{x=1}^4sqrt{1 + left ( frac{dy}{dx} right )^2}dx) ( = sqrt{2} int_{x=1}^{4} dx ) ( = sqrt{2} left [ x right ]_1^4) ( = sqrt{2}(4-1)) ( = 3sqrt{2}) Thus, the arc length of the arc of y2 = x2 from (1, 1) to (4, 8) is ( = 3sqrt{2}) unit.

Find the length of the arc of the semi cubical parabola y² = x² between the points (1,1) and (4,8)

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Find the length of the arc of the semi cubical parabola y2 = x2 between the points (1,1) and (4,8)

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Find the length of the arc of the semi cubical parabola y² = x² between the points (1,1) and (4,8)