Do the following for the given curve on the given interval. a. Set up an integral for

pancha3 2021-09-11 Answered
Do the following for the given curve on the given interval.
a. Set up an integral for the length of the curve.
b. Graph the curve to see what it looks like.
c. Use your​ graphers
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Macsen Nixon
Answered 2021-09-12 Author has 117 answers

dydx=ddx(sin{x}cos{x})
=cos{x}[x(sin{x})+cos{x}]
=cos{x}+2sin{x}+cos{x}
=2cos{x}+xsin{x}
a) set up integral
L=02π(1+dxdy}2dx
=02π(1+2cos{x}+{x}sin{x})2dx
=02π1+4cos{x}+x2sin2x+4xcos{x}sin{x}
b)
image
c) λ=02π1+(dydx)2
=02π1+(2cos{x}+xsin{x})2dx
=02π1+4cos2{x}+x2sin2{x}+4xcos{x}sin{x}
[121+4cos2{x}+x2<

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