The equation for length of a curve: what are the integral ends?

[Cloudless]

Homework Statement

The given curve is r(t) = <t², 2t, -3>

Write an equation for the length of the curve from <0,0,-3> to <1, 2, -3>



2. The attempt at a solution

I take the derivative of r(t) for r'(t), then plug it into the length formula.

L = ∫ of √( (2t)² + 2² )

For the Integral, I put from 0 to 1, because in the original equation, the x component t² = 1 when t is 1, and the y component 2t = 2 when t is 1.

Am I doing something wrong? o_o

 

[Dick]

Homework Statement

The given curve is r(t) = <t², 2t, -3>

Write an equation for the length of the curve from <0,0,-3> to <1, 2, -3>



2. The attempt at a solution

I take the derivative of r(t) for r'(t), then plug it into the length formula.

L = ∫ of √( (2t)² + 2² )

For the Integral, I put from 0 to 1, because in the original equation, the x component t² = 1 when t is 1, and the y component 2t = 2 when t is 1.

Am I doing something wrong? o_o

Seems ok to me. Why do you think you are doing something wrong?

 

[Cloudless]

Ah ok. The notes never fully explained it so I was doing it by instinct mostly. xD

Thanks

 

[1994Bhaskar]

dunno