Area under a Parametric Curve | Formula, Derivation, & Example

In Calculus I, we computed the area under the curve where the curve was given as a function y=f(x). Now we extend the ideas to parametric curves, coming up with a new formula based on a substitution. After deriving the formula, we apply it to a specific example.

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This video was created by Dr. Trefor Bazett

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[andrewharrison]

So much to think about in under 6 minutes - not much/any wasted time in this one - excellent

[AntonioMac]

Super good explanation on how you derived the formula, I was looking exactly for this awesome content! THank you!

[potrkca]

excellent breakdown of how to derive this formula - thank you!

[bobprior]

This is a good explanation of the area of that region ... except for one thing. The value of at the end does matter because when calculated, it is negative. To make it positive—which it should be, and not just by taking the absolute value of it—we must either use the top half (Quadrant I portion of the curve) or the bottom half (Quadrant IV portion of the curve). Because the height of the rectangle is y, using the top half we must use negative root 3 as the upper limit; if we use the bottom half, we can use positive root 3 as the upper limit, but we must negate the value of y to make the integral positive.
By the way, I really like your videos and am recommending them to my students.

[xuepingsong]

Is f required to be invertible? If so, what happens when the curve loops back and forth?

[thomasolson]

What about the unit analysis if this was a physics question in some kind of weird space?

[dharshan.m]

Please upload for cartisian and polar curve

[Tony-uppz]

there is a mistake, but it is a good lesson

[chaotickreg]

Couldn't you integrate from -sqrt(3) to sqrt(3) instead of multiplying the top half by 2? Surely there are functions where the enclosed area has no axis of symmetry.

[ДенисКрохмаль-ье]

Спасибо.... я даже не понимая слов все понял))))

[mahnoorawan]

Salam sir
I am mahnoor mathematics student can u help me sir plz reply I have a problem in my assignment