Find the Exact Value Of $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 14

Short Answer

Find the exact value of $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ where $\mathbf { F } ( x , y ) = e ^ { x - 1 } \mathbf { i } + x y \mathbf { j }$ and C is given by $\mathbf { r } ( t ) = 2 t ^ { 2 } \mathbf { i } + 7 t ^ { 3 } \mathbf { j } , 0 \leq t \leq 1$

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Definitions:

Water Footprint

The total volume of fresh water used to produce goods or services by a company, individual, or nation.

Heat Energy

The form of energy that is transferred between systems or objects with different temperatures, also known as thermal energy.

Polluter

An entity (individual, company, or other organization) that releases pollutants into the environment, causing pollution.

Pollution

The introduction of contaminants into the natural environment that cause adverse change, affecting air, water, and soil quality.