Set Up an Integral for the Length of the Curve $$x = \sin 5 y , - \pi \leq y \leq 0$$

question 12

Multiple Choice

Set up an integral for the length of the curve.
- $$x = \sin 5 y , - \pi \leq y \leq 0$$

• A) \(\int _ { - \pi } ^ { 0 } \sqrt { 1 + \cos ^ { 2 } 5 y } d y\)
• B) \(\int _ { - \pi } ^ { 0 } \sqrt { 1 + 25 \sin ^ { 2 } 5 y } d y\)
• C) \(\int _ { - \pi } ^ { 0 } \sqrt { 1 + 25 \cos ^ { 2 } 5 y } d y\)
• D) \(\int _ { - \pi } ^ { 0 } \sqrt { 1 + 5 \cos 5 y } d y\)

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Definitions:

Ozonolysis-Reduction

A two-step chemical reaction that first involves the cleavage of alkenes with ozone to form carbonyl compounds, followed by reduction.

Alkene

Hydrocarbons containing at least one carbon-to-carbon double bond, characterized by the formula CnH2n.

Products

The substances that result from a chemical reaction, situated on the right side of a chemical equation.

Compound

A substance made up of atoms of two or more different elements chemically bonded together.