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Find the length of the curve. x=12t³, y= 18t², 0≤t≤ √8 is ___

User Funkysoul
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1 Answer

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Final answer:

The length of the curve given by the parametric equations x=12t^3 and y=18t^2 from t=0 to t=\sqrt{8} can be determined using the arc length formula for parametric curves, by integrating the square root of the sum of the squares of the derivatives of x and y with respect to t.

Step-by-step explanation:

To find the length of the curve with the given parametric equations x=12t^3 and y=18t^2 from t=0 to t=\sqrt{8}, we need to use the formula for the arc length of a curve defined by parametric equations:

The formula for the arc length, L, is:

L = \int from a to b \sqrt((dx/dt)^2 + (dy/dt)^2) dt

First, we calculate the derivatives of x and y with respect to t:

dx/dt = 36t^2

dy/dt = 36t

Now we plug these into the arc length formula and integrate from 0 to \sqrt{8}:

L = \int from 0 to \sqrt{8} \sqrt((36t^2)^2 + (36t)^2) dt

This integral will yield the length of the curve.

User Perusopersonale
by
7.9k points
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