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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
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