kayleeblanton8140 kayleeblanton8140
  • 08-05-2018
  • Mathematics
contestada

Set up an integral to find the length of the path x = sin(t), y = sin2 (t). hint: first you need to find an interval that traces the path exactly once.

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wizard123
wizard123 wizard123
  • 08-05-2018
The path goes from x =-1 to 1, therefore t = -pi/2 to pi/2

Arc length is defined as:
[tex]\int \sqrt{(\frac{dx}{dt})^2 +(\frac{dy}{dt})^2} dt[/tex]

Answer:
[tex]\int_{-\pi/2}^{\pi/2} \sqrt{cos^2 (t) + 4sin^2(t) cos^2(t)} dt[/tex] 
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good job