Use Stoke's Theorem to Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 90

Multiple Choice

Use Stoke's theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ where $\mathbf { F } ( x , y , z ) = e ^ { - 7 x } \mathbf { i } + e ^ { 4 y } \mathbf { j } + e ^ { 5 x } \mathbf { k }$ and C is the boundary of the part of the plane $8 x + y + 8 z = 8$ in the first octant.

• A) 69
• B) 16
• C) 49
• D) 0
• E) 23

---

Definitions:

Bond Portfolios

Collections of bonds held by investors or institutions, designed to achieve certain financial goals while managing risk and return.

Indexing

The investment strategy of replicating the performance of a market index, often through passive fund management.

Duration

A measure of the sensitivity of the price of a bond or a fixed income portfolio to changes in interest rates.

Interest-Rate Risk

The possibility of incurring losses in investments as a result of variations in interest rates, especially impacting fixed-income securities.