Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 172

Short Answer

Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $\mathbf { F } ( x , y ) = e ^ { x } \mathbf { i } + x y \mathbf { j }$ and the curve $C$ is given by the vector function $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + t ^ { 3 } \mathbf { j } , \quad 0 \leq t \leq 1$ .

---

Definitions:

Fireworks

Explosive devices used primarily for entertainment purposes, emitting light, noise, smoke, and various colors when ignited.

Guaranteed Insurability

An insurance policy feature that allows the policyholder to buy additional coverage without proof of insurability at designated times.

Life Insurance

A contract between an insurer and a policyholder in which the insurer guarantees payment of a death benefit to named beneficiaries upon the death of the insured.

Insured

A person, company, or entity covered under an insurance policy to receive compensation for a specified loss or damage.