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Find the exact length of the curve y = 2 8x^(3/2), 0 ≤ x ≤ 1?

User Art Swri
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Final answer:

To find the exact length of the curve y = 28x^(3/2), we use the arc length formula and evaluate the integral.

Step-by-step explanation:

To find the exact length of the curve y = 28x^(3/2), we need to use the arc length formula. The formula is given by L = int(a to b) sqrt(1 + (dy/dx)^2) dx, where a and b are the limits of integration. In this case, a = 0 and b = 1.

We first find dy/dx by taking the derivative of y with respect to x. dy/dx = 3sqrt(2)x^(1/2).

Substituting this into the arc length formula and integrating, we get L = int(0 to 1) sqrt(1 + (3sqrt(2)x^(1/2))^2) dx.

Simplifying the expression inside the square root, we have L = int(0 to 1) sqrt(1 + 18x) dx.

Evaluating the integral gives us the exact length of the curve.

User DanScan
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