Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + 4 \cos t \mathbf { j } + 4 \sin t \mathbf { k } , 0 \leq t \leq 2 \pi$

question 31

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + 4 \cos t \mathbf { j } + 4 \sin t \mathbf { k } , 0 \leq t \leq 2 \pi$
Select the correct answer.

• A) \(2 \sqrt { 5 } \pi\)
• B) \(4 \sqrt { 5 } \pi\)
• C) \(2 \sqrt { 6 } \pi\)
• D) \(\sqrt { 6 } \pi\)

---

Definitions:

Trial Balance

A bookkeeping worksheet in which the balances of all ledgers are compiled into debit and credit account column totals that are equal.

Uncollectable Account

A debt or receivable that is considered to be uncollectible from a debtor, often because it is overdue or the debtor is unable to pay.

Collection Agency

An enterprise that seeks to collect payments from individuals or businesses on outstanding debts.

Pegboard System

A bookkeeping system that uses a lightweight board with pegs on which forms can be stacked, allowing each transaction to be entered and recorded on four different bookkeeping forms at once; also called the one-write system.