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Welcome to March Calculus Madness!
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Let:
x(t) = a * cos t
y(t) = b * sin t
Then:
∫ y(x) dx = ∫ y(t) * x'(t) dt
x'(t) = -a * sin t
And:
∫ y(t) * x'(t) dt
= ∫ -a * sin t * b * sin t dt
= -a * b * ∫ sin^2 t dt
= -a * b * ∫1/2 - 1/2 * cos(2*t) dt
= -a * b * (t/2 - sin(2*t)/4) + C
That wraps up March Calculus Madness 2022.
Next Post: April 9, 2022
Have a great day and hope you enjoyed the series!
Eddie
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
