2. Consider the curve $r = 2 \cos 3\theta$ shown below. A. Find the area the curve encloses. Show all work. B. Set up a definite integral that will give the length of the curve. Show all work. C. Approximate the length of the curve using Trapezoids with 4 subdivisions. Show all work.
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Step 1: The area enclosed by a polar curve $r = f(\theta)$ is given by: $$A = \frac{1}{2} \int_{\alpha}^{\beta} [f(\theta)]^2 d\theta$$ where $\alpha$ and $\beta$ are the angles that define the curve. Show more…
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