Set Up, but Do Not Evaluate, an Integral for the Length

question 2

Multiple Choice

Set up, but do not evaluate, an integral for the length of the curve. $y=2 e^{x} \sin x, \quad \quad 0 \leq x \leq \frac{9 \pi}{2}$

• A) \(L=\int_{0}^{9 x / 2} \sqrt{1-4 e^{2 x}(1+\sin 2 x)} d x\)
• B) \(L=\int_{0}^{9 x / 2} \sqrt{1+4 e^{2 x}(1-\sin x)} d x\)
• C) \(L=\int_{0}^{9 x / 2} \sqrt{1-4 e^{2 x}(1-\sin 2 x)} d x\)
• D) \(L=\int_{0}^{9 x / 2} \sqrt{1+4 e^{2 x}(1-\sin 2 x)} d x\)
• E) \(L=\int_{0}^{9 x / 2} \sqrt{1+4 e^{2 x}(1+\sin 2 x)} d x\)

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Definitions:

Probability Distribution

A description of how the probabilities are distributed over the values of the random variable.

Sample Mean

The average calculated from a sample of data, representing the central point or typical value of the sample.

Population Mean

The average of all the values in a population, representing the central point of a data set.

Parameters

Quantitative characteristics that define or summarize features of a population in statistical analysis.