Question

step 1
if ( g(x) ) is positive, then the integral ( int_{a}^{b} g(x) d x ) corresponds to the area beneath ( g(x) ) and above the ( x )-axis over the interval (a, b).
on (0,8), the function ( g(x) ) is above the ( x )-axis and is therefore positive. thus, ( int_{0}^{8} g(x) d x ) equals the area of the triangle created by the function, the ( x )-axis, and the ( y )-axis.
this triangle is a right triangle with a side length of 8 along the ( x )-axis and a side length of 10 along the ( y )-axis. (give the numeric values.)
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Explanation:

Step1: Determine the base of the triangle

The base of the triangle is along the \(x -\)axis. The interval is \([0,8]\), so the length of the base \(b = 8\).

Step2: Determine the height of the triangle

From the graph (implied by the integral context), assume the function \(g(x)\) forms a right - triangle. If we consider the standard form of a linear function \(y=mx + c\) and the integral interpretation. For a right - triangle formed by \(y = g(x)\), \(x = 0\), \(x = 8\) and \(y = 0\), if we assume \(g(x)\) is a linear function passing through \((0,0)\) and \((8,10)\) (common in basic integral - area - triangle problems, and since the user might have a graph where the \(y -\)intercept is \(0\) and at \(x = 8\), \(y=10\)). The height \(h\) of the triangle (along the \(y -\)axis) is \(10\).

Answer:

The side length along the \(x -\)axis is \(8\) and along the \(y -\)axis is \(10\).