6.3 Notes

# 6.3 Notes - Arc Length(Section 6.3 Let C be a curve dened...

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Arc Length (Section 6.3) Let C be a curve defined by the parametric equations x = f ( t ) and y = g ( t ) for a t b , where f and g have continuous first derivatives. Then the length of C is: L = Z b a s dx dt 2 + dy dt 2 dt L is how long the curve is if you imagine it stretched out in a straight line segment. Example 0.1. Find the length of x = cos t , y = t + sin t on 0 t π . What if we have y = f ( x ) on an interval a x b with f continuously dif- ferentiable? This is a special case of the above formula where x = t and y = f ( t ). Then L = Z b a s 1 + dy dx 2 dx Example 0.2. Find the length of

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