Find Arc Length Using Trapezoids

In summary, the formula for finding arc length using trapezoids is: L = (b<sub>1</sub> + b<sub>2</sub>) x h / 2. To measure the parallel sides of a trapezoid, a ruler or measuring tape can be used. This method can only be used for shapes that can be approximated by a trapezoid, such as circular arcs. The accuracy of this method depends on the number of trapezoids used, but there are other methods available, such as using calculus or the arc length formula for a circle. However, the trapezoid method is a simpler and more accessible option for those without a strong math background.
  • #1
nyyfan0729
12
0
Using trapezoids and N=4, find the length of the arc of the curve y=(1/3)x^3 from (0,0) to (1,1/3).
 
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  • #2
Of course, [itex]\frac{dy}{dx}= x^2[/itex] so the length of the curve from x= 0 to x= 1 is
[tex]\int_0^1 \sqrt{1+ x^4}dx[/tex]

By "Using trapezoids" do you mean use the trapezoid rule to numerically integrate that?
 

1. What is the formula for finding arc length using trapezoids?

The formula for finding arc length using trapezoids is:
L = (b1 + b2) x h / 2
where L is the arc length, b1 and b2 are the lengths of the two parallel sides of the trapezoid, and h is the height of the trapezoid.

2. How do you measure the parallel sides of a trapezoid for finding arc length?

To measure the parallel sides of a trapezoid, you can use a ruler or measuring tape. Place one end of the ruler or tape at the bottom of one parallel side and measure to the bottom of the other parallel side. Make sure to use the same unit of measurement for both sides.

3. Can you use this method to find the arc length of any shape?

No, this method can only be used to find the arc length of shapes that can be approximated by a trapezoid. It is most commonly used for circular arcs, where the trapezoid is a good approximation of the curve.

4. How accurate is this method for finding arc length?

The accuracy of this method depends on the number of trapezoids used to approximate the arc. The more trapezoids used, the closer the approximation will be to the actual arc length. However, using too many trapezoids can be time-consuming and may not significantly improve the accuracy.

5. Are there other methods for finding arc length?

Yes, there are other methods for finding arc length, such as using calculus or using the arc length formula for a circle, L = 2πrθ/360, where r is the radius of the circle and θ is the central angle in degrees. However, the trapezoid method is a simpler and more accessible method for those without a strong math background.

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