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Find the length of the cardioid, r=3+3 cosine theta, from (0,2pi)

Question:

Find the length of the cardioid, r=3+3 cosine theta, from (0,2{eq}\pi {/eq})

Arc Length:

In order to calculate the arc length, it must be understood that the length depends on the derivative of expression under calculation between two different inputs represented as bounds. In polar coordinates, the arc length is defined as {eq}L = \int_a^b \sqrt{r^2+(\frac{dr}{d\theta})^2} d\theta {/eq}.

Answer and Explanation:

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Given: {eq}r = 3+3\cos(\theta) \\ (0,2\pi) {/eq}


To calculate the arc length, the arc length formula for polar coordinates ({eq}L = \int_a^b...

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Cardioid in Math: Definition, Equation & Examples

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Chapter 1 / Lesson 13
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This lesson will cover a neat shape studied in upper-level mathematics called a cardioid. We will look at the basic shape, how it is constructed, its equation in polar form, and various examples of these equations and corresponding cardioids.


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