Arc Length of a Polar Curve

This video explains how to determine the arc length of a polar curve.

[Mathispoweru]

Yes, the integrand would be sqrt( theta^2 + 1), then we'd have to use trig substitution.

Let theta = tan(x) d(theta) = sec^2(x) dx

[inukai]

When you integrate a function from a to b, you subtract F(b)-F(a) (where F is the integrated function) In this graph F(0) And F(2pi) are the same value because sin(0) = sin(2pi) so you will always get 0 unless you use the property of symmetrical graphs.

[emanuelrgz]

Excellent work, nice technique of integration too!!

[beks]

Thanks for this video. It was sooo helpful

[inukai]

No, the square roots would only cancel if the values were the same. He multiplied sqrt(2+2sin(theta)) and sqrt(2-2sin(theta)). since 2+2sin(theta) does not equal 2-2sin(theta) they cannot be combined like that.

[benicia]

They use ur videos as examples on my honeworks

[inukai]

It would be the same except you wouldn't include the stuff about symmetry. Since the spiral is not symmetrical it would be plain old integration from 0 to 2pi.

[XxjLumaXx]

Why don't you change the limits? Don't you change them since you used u substitution?

[Krisbg]

IS THERE A VIDEO THAT DERIVES THE FORMULA??

[viczhou]

Why come when I try to find the definite integral of sqrt (2-2sinx) from 0 to 2 pi is zero? Is that integral the same as your integral from -pi/2 to pi/2?

[anzatzi]

Why not derive the formula? Otherwise its just an algebra fest with no meaning or motivation. Microcosm of whats wrong with math education