Find the exact length of the curve.   36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

Trigonometry (MindTap Course List)
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Chapter6: Topics In Analytic Geometry
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Find the exact length of the curve.

 

36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

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36y^2=\left(x^2-4\right)^3

y^2=\frac{\left(x^2-4\right)^3}{36}

y=\pm\sqrt{\frac{\left(x^2-4\right)^3}{36}}

but here y\geq 0

y=\sqrt{\frac{\left(x^2-4\right)^3}{36}}

y=\frac{\sqrt{\left(x^2-4\right)^3}}{6}

y=\frac{\left(x^2-4\right)^{\frac{3}{2}}}{6}

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