Find the Length of the Curve $\mathbf { r } ( t ) = \langle 2 t , \sin t , \cos t \rangle , 0 \leq t \leq 2 \pi$

question 89

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = \langle 2 t , \sin t , \cos t \rangle , 0 \leq t \leq 2 \pi$

• A) \(2 \pi \sqrt { 2 }\)
• B) \(\pi \sqrt { 10 }\)
• C) \(2 \pi \sqrt { 3 }\)
• D) \(\pi \sqrt { 14 }\)
• E) \(4 \pi\)
• F)
• \(3 \pi \sqrt { 2 }\)
• G) \(2 \pi \sqrt { 5 }\)

---

Definitions:

Macroeconomics

The branch of economics that studies the behavior and performance of an economy as a whole, focusing on total national income, employment, and price levels.

Equilibrium Price

The price at which the quantity of a good or service supplied is equal to the quantity demanded, resulting in market balance.

Economics

The social science that studies the production, distribution, and consumption of goods and services.

Microeconomics

The branch of economics that focuses on the actions of individuals and industries, like the dynamics between buyers and sellers, and the factors that influence the choices of individuals and businesses.