____ Show That $\mathbf { F }$ Is Conservative and Find a Function

question 35

Multiple Choice

____ Show that $\mathbf { F }$ is conservative and find a function $f$ such that $\mathbf { F } = \nabla f$ , and use this result to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $C$ is any path from $A \left( x _ { 0 } , y _ { 0 } \right)$ to $B \left( x _ { 1 } , y _ { 1 } \right)$ .
$\mathbf { F } ( x , y ) = \left( 15 x ^ { 2 } y ^ { 2 } - 14 x y ^ { 4 } \right) \mathbf { i } + \left( 10 x ^ { 3 } y - 28 x ^ { 2 } y ^ { 3 } \right) \mathbf { j } ; A ( 1 , - 2 )$ and $B ( 1 , - 1 )$

• A) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 34\)
• B) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 90\)
• C) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = - 144\)
• D) \(\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 118\)

---

Definitions:

Unearned Rent

Income received for rent before the rental period has occurred, recorded as a liability until the period passes.

Adjusted Trial Balance

A listing of all the accounts and their balances after adjustments have been made, used to prepare financial statements.

Retained Earnings

The portion of net income that is kept by a company to reinvest in its core business or to pay debt, rather than being distributed to shareholders as dividends.

Revenue Accounts

Accounts that track the income generated from the sale of goods and services, investments, and other sources during the accounting period.