Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$

question 123

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j }$ on a particle that moves along the curve $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 1 \leq t \leq 2$ .

• A) \(127\)
• B)\(128\)
• C) \(63\)
• D) \(64\)
• E) \(31\)
• F)\(32\)
• G) \(15\)
• H)\(16\)

---

Definitions:

Brand New

Something that is completely new and has not been used or seen before.

Financial Budgets

Detailed forecasts of an organization's income, expenditures, and capital for a set period, guiding fiscal planning and control.

Cash Flows

The total amount of money being transferred into and out of a business, especially affecting liquidity.

Expenditures

Money spent by an organization or individual for goods, services, or other purposes.