the graph of g is comprised of a semi - circle and line segments. evaluate the definite integral of ∫₁₅¹⁷…

Explanation:

Step1: Identify the geometric shape

The region under the curve from $x = 15$ to $x=17$ is a right - triangle.

Step2: Determine base and height

The base of the triangle is $b=2$ (since $17 - 15=2$), and from the graph, the height $h = 4$.

Step3: Use the area formula for a triangle

The area of a triangle is $A=\frac{1}{2}bh$. Substituting $b = 2$ and $h = 4$ gives $A=\frac{1}{2}\times2\times4$. $A = 4$ Since the definite integral $\int_{a}^{b}g(x)dx$ represents the net - signed area between the curve $y = g(x)$ and the $x$ - axis from $x=a$ to $x = b$, and the region is above the $x$ - axis (so the area is positive).

Answer:

$4$