- #1
2^Oscar
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Hey guys,
Got a bit of a problem with a question I found in a textbook. I can do most of it but there's one little part I'm really struggling with:
A curve C is given parametrically by:
The length of arc C measured from the point (0,1) to a general point with parameter t is s. Find s in terms of t and deduce that, for any point on the curve, y=e-s.I'm happy finding that the arc length is defined as [tex]\int (tanht)dt[/tex] between the limits of 0 and s, and i evaluate this integral to be ln(coshs) however after this I am stumped; I am having great trouble getting to y=e-s.Can anyone please help me out?Oscar
Got a bit of a problem with a question I found in a textbook. I can do most of it but there's one little part I'm really struggling with:
A curve C is given parametrically by:
x=t-tanht, y=secht, t[tex]\geq0[/tex]
The length of arc C measured from the point (0,1) to a general point with parameter t is s. Find s in terms of t and deduce that, for any point on the curve, y=e-s.I'm happy finding that the arc length is defined as [tex]\int (tanht)dt[/tex] between the limits of 0 and s, and i evaluate this integral to be ln(coshs) however after this I am stumped; I am having great trouble getting to y=e-s.Can anyone please help me out?Oscar
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