Find the length {eq}L {/eq} of the curve {eq}\; \mathrm{R}(t) = 3t^2 \mathrm{i} + 2t^3 \mathrm{j} - \mathrm{k} \; {/eq} over the interval {eq}\; [2, \; 4] {/eq}.
Question:
Find the length {eq}L {/eq} of the curve {eq}\; \mathrm{R}(t) = 3t^2 \mathrm{i} + 2t^3 \mathrm{j} - \mathrm{k} \; {/eq} over the interval {eq}\; [2, \; 4] {/eq}.
Arc Length:
To find the arc length we will use the formula {eq}\int \sqrt{\left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )^{2} +\left ( \frac{\mathrm{d} y}{\mathrm{d} t} \right )^{2}+\left ( \frac{\mathrm{d} z}{\mathrm{d} t} \right )^{2}}dt {/eq}
Answer and Explanation: 1
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View this answerTo find the length of the curve, we will use the formula {eq}x=3t^{2}\\ y=2t^{3}\\ z=-1\\ \frac{\mathrm{d} x}{\mathrm{d} t}=6t\\ \frac{\mathrm{d}...
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Chapter 9 / Lesson 10Learn how to find the arc length of a sector with the formula and examples. Understand the formula and the method to find the area of a sector with examples.