Let x = 2t^2, y = (3/2)t^2 t = [3,5] I have to find to length of the curve from these equations using integration, without eliminating parameters. Then I need to sketch it having eliminated parameters, and finally, find the length using algebra.
Last edited by yuropod; April 26th 2009 at 10:12 PM.
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Originally Posted by yuropod Let I have to find to length of the curve from these equations using integration, without eliminating parameters. Then I need to sketch it having eliminated parameters, and finally, find the length using algebra. . As . Use the arc length formula: ------------------------------------ (This is the equation of the line you want to sketch.) Using again, we have Using the Pythagorean Theorem, we have the length of this line to be which agrees with the above answer.
Thanks a bunch!
Hello, yuropod! Let: . Find the length of the curve without eliminating parameters. Formula: . We have: . . . Then: . . . Hence: . Therefore: .
Originally Posted by yuropod Let x = 2t^2, y = (3/2)t^2 t = [3,5] I have to find to length of the curve from these equations using integration, without eliminating parameters. Then I need to sketch it having eliminated parameters, and finally, find the length using algebra. It's in fact the straight line y=3x/4 from (18,27/2) to (50,75/2) . So we can use the distance between the two pionts to find the length.
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