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

question 22

Multiple Choice

Set up, but do not evaluate, an integral for the length of the curve.
$y = 6 e ^ { x } \sin x , \quad 0 \leq x \leq \frac { 9 \pi } { 2 }$

• A) \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)
• B) \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 + \sin 2 x ) } d x\)
• C)
• \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 - 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• D)
• \(L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin 2 x ) } d x\)
• E)
• \[L = \int _ { 0 } ^ { 9 x / 2 } \sqrt { 1 + 36 e ^ { 2 x } ( 1 - \sin x ) } d x\]

---

Definitions:

Short-term Financing

Refers to the obtaining of loans or other monetary support for a period of typically less than one year, to address immediate financial needs.

Long-term Financing

Funding obtained for a time frame exceeding one year in duration, typically used for acquiring or investing in assets that have a long useful life.

Carrying Costs

Expenses associated with holding inventory, including storage, insurance, and opportunity costs, impacting a company's financial performance.

Orders

Directions or commands given by authority, or customer requests for goods or services.