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# Curves

### Find the area under the curve

Find the area under the curve y=4x+1 from x=2 to x=6

### Intersection of Curves

Find the points of intersection (if any) of the given pair of curves and draw the graphs. Y= x^2 and y= 2x+2

### Example of a non-rectifiable closed Jordan curve.

Give an example of a non-rectifiable closed Jordan curve on the interval -1<=t<=1. My thought: t + i(sin 1/t) + ????? Please advise what curve I can add to make this work. Or, if this will not work, please provide an example of a non-rectifiable closed Jordan curve on -1<=t<1.

### Curves

#26 Please see the attached file for full problem description.

### Length of an arc - when will a person leave your view?

Two people 1.8m tall walk from each other until they can no longer see each other (due to the curvature of the earth which has a radius of 6378km). Assuming nothing else blocks their view, how far do they have to walk? Note. I cant get my head around how this relates to what we've lear

### Length of Curve/Calc II problem

Find the length of the curve y=cosh(x) between x=-1 and x=2 Find the length of y=cosh x for -1 ≤ x ≤ 2. The length of the curve will be given by : = sinh x Length = Integral is given by : Therefore length = = .0528

### Curvature of the curve and torsion of the curve

Differential Geometry (I) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( &#8730;6 at^3, a(1+3t^2), &#8730;6 at ) Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = tors