Find a Function $f$ Such That $\mathbf { F } = \nabla f$

question 94

Short Answer

Find a function $f$ such that $\mathbf { F } = \nabla f$ and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve $C$ .
$$\mathbf { F } ( x , y ) = y \mathbf { i } + ( x + 10 y ) \mathbf { j }$$
$C$ is the upper semicircle that starts at $( 1,2 )$ and ends at $( 5,2 )$ .

Solve simple radical equations.

Apply the Pythagorean theorem to find missing values in geometric figures.

Use graphing calculators for solving equations.

Understand and apply basic principles of complex numbers in standard form.

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