Evaluate $\int _ { - c } x \vec { i } + ( y + 10 x ) \vec { j } + ( z + 9 x ) \vec { k } \cdot \overrightarrow { d r }$

question 64

Short Answer

Evaluate $\int _ { - c } x \vec { i } + ( y + 10 x ) \vec { j } + ( z + 9 x ) \vec { k } \cdot \overrightarrow { d r }$ , where C is the curve $\vec { r } ( t ) = t \vec { i } + ( 1 - t ) \vec { j } + \left( t ^ { 2 } + 3 \right) \vec { k }$ for 0 $\le$ t $\le$ 1.
Note that the line integral is around -C, not C.

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Definitions:

Metals

Elements that typically have a shiny surface and can conduct electricity and heat efficiently.

Electromagnet

A type of magnet in which the magnetic field is produced by an electric current, which can be turned on or off.

AC Line

A conductor or conductors that carry alternating current (AC) electricity from the power source to the load.

Demagnetized

The state of a magnetic material where it has lost its magnetization, either partially or completely.