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

pancha3

pancha3

Answered question

2021-09-11

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

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-09-12Added 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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