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## Homework Statement

A cable hangs between two poles of equal height and 39 feet apart.

At a point on the ground directly under the cable and

x feet from the point on the ground halfway between the poles

the height of the cable in feet is

h(x)=10 +(0.4)( x^{1.5})

The cable weighs 12.5 pounds per linear foot.

Find the weight of the cable.

## Homework Equations

The Arc Length Formula

## The Attempt at a Solution

I need to find the length of the cable to determine the weight. However, since the problem mentions a variable, x, is the "from the point on the ground halfway between the poles," x must be 0. So the bounds of integration are from 0 to 39/2. After finding h'(x) and plugging it into the arc length formula and evaluating the integral from 0 to 39/2, I multiplied my answer by 2 to get the full length of the arc. Once I got this I found the weight to be some absurd number around 1000.

So where did I go wrong (assuming my differentiation, integration and calculations are correct)?