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Define arc length.

The distance between two points along a curve.

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Define arc length.

The distance between two points along a curve.

What is a parametric curve?

A curve where the x and y coordinates are defined by functions of a parameter, usually denoted as t.

Define a smooth planar curve.

A curve in a plane that has a continuous first derivative.

Arc length formula for parametric curves?

$S=\int_a^b \sqrt{(\tfrac{dx(t)}{dt})^2 + (\tfrac{dy(t)}{dt})^2} dt$

Arc length formula for Cartesian curves?

$S=\int_a^b \sqrt{1+[f'(x)]^2} dx$

Steps to find arc length of parametric curve?

Find dx/dt and dy/dt. 2. Substitute into the arc length formula. 3. Evaluate the integral.

How to evaluate $\int_0^\pi \sqrt{1} dt$ ?

All Flashcards

Define arc length.

The distance between two points along a curve.

What is a parametric curve?

A curve where the x and y coordinates are defined by functions of a parameter, usually denoted as t.

Define a smooth planar curve.

A curve in a plane that has a continuous first derivative.

Arc length formula for parametric curves?

$S=\int_a^b \sqrt{(\tfrac{dx(t)}{dt})^2 + (\tfrac{dy(t)}{dt})^2} dt$

Arc length formula for Cartesian curves?

$S=\int_a^b \sqrt{1+[f'(x)]^2} dx$

Steps to find arc length of parametric curve?

Find dx/dt and dy/dt. 2. Substitute into the arc length formula. 3. Evaluate the integral.

How to evaluate $\int_0^\pi \sqrt{1} dt$ ?