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Unit: Parametric equations, polar coordinates, and vector-valued functions

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Arc length: parametric curves

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Practice

Parametric curve arc lengthGet 3 of 4 questions to level up!

Planar motion

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Planar motion (with integrals)
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Planar motion (with integrals)Get 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 160 Mastery points

Area: polar regions (single curve)

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Area bounded by polar curves introGet 3 of 4 questions to level up!
Area bounded by polar curvesGet 3 of 4 questions to level up!

Area: polar regions (two curves)

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Worked example: Area between two polar graphs
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Area between two polar curvesGet 3 of 4 questions to level up!

Arc length: polar curves

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Arc length of polar curvesGet 3 of 4 questions to level up!

Calculator-active practice

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Evaluating definite integral with calculator
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Area with polar functions (calculator-active)Get 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 400 Mastery points

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Unit test

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About this unit

We are used to working with functions whose output is a single variable, and whose graph is defined with Cartesian, i.e., (x,y) coordinates. But there can be other functions! For example, vector-valued functions can have two variables or more as outputs! Polar functions are graphed using polar coordinates, i.e., they take an angle as an input and output a radius! Learn about these functions and how we apply the concept of the integral on them.