Difference between revisions of "Length of a curve"
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length = <font size = "+2"><span>∫</span></font>sqr(1+f '(x)<sup>2</sup>)dx | length = <font size = "+2"><span>∫</span></font>sqr(1+f '(x)<sup>2</sup>)dx | ||
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| + | For the previous example of heating a liquid, the first derivative of the equation was f '(t)=30e<sup>−0.3t</sup> | ||
| + | |||
| + | so the length of the curve from 0 to 5 minutes would be: | ||
| + | |||
| + | <font size = "+2"><span>∫</span></font>sqr(1+30e<sup>−0.3t</sup><sup>2</sup>)dt | ||
Revision as of 17:39, 1 April 2021
The length of a curve from point a to point b can be found using an integral of the first derivative of the equation:
equation = f(x)
first derivative = f '(x)
length = ∫sqr(1+f '(x)2)dx
For the previous example of heating a liquid, the first derivative of the equation was f '(t)=30e−0.3t
so the length of the curve from 0 to 5 minutes would be:
∫sqr(1+30e−0.3t2)dt
