Integrate the function f over the given region. f(x,y) = \frac{x}{6} + \frac{y}{2} over the...


Integrate the function {eq}f {/eq} over the given region.

{eq}f(x,y) = \frac{x}{6} + \frac{y}{2} {/eq} over the trapezoidal region bounded by the {eq}x- {/eq}axis, {eq}y- {/eq}axis, line {eq}x =6 {/eq}, and line {eq}y = - \frac{1}{3}x + 4 {/eq}.

A. 18

B. 22

C. 30

D. 46

Evaluating the Integral:

The objective is to evaluate the integral function by using the given function.

The given functions are {eq}f\left ( x, y \right ) = \frac{x}{6} + \frac{y}{2} {/eq}

The general form of integration is {eq}\iint_{R} f\left ( x, y \right ) dy dx {/eq}

And by using the given region we have to integrate the function and find the result.

Answer and Explanation:

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Given that:

{eq}f\left ( x, y \right ) = \frac{x}{6} + \frac{y}{2} {/eq}

The region is bounded in both {eq}x \ and y {/eq} axis.

The limits are:


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