Thursday, March 31, 2022

March Calculus Madness Sweet Sixteen - Day 16: A Parametric Integral Example

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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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