the accompanying figure shows the area of regions bounded by the graph of f and the x - axis. evaluate the…

the accompanying figure shows the area of regions bounded by the graph of f and the x - axis. evaluate the following integral. \n int_{0}^{a}f(x)dx \n int_{0}^{a}f(x)dx=square \text{ (simplify your answer.)}

the accompanying figure shows the area of regions bounded by the graph of f and the x - axis. evaluate the following integral. \n int_{0}^{a}f(x)dx \n int_{0}^{a}f(x)dx=square \text{ (simplify your answer.)}

Answer

Explanation:

Step1: Recall integral - area relationship

The definite integral $\int_{0}^{a}f(x)dx$ is equal to the net - area between the curve $y = f(x)$ and the $x$ - axis from $x = 0$ to $x=a$. Areas above the $x$ - axis are positive and areas below the $x$ - axis are negative.

Step2: Identify positive and negative areas

The area above the $x$ - axis from $x = 0$ to some point is $20$, and the area below the $x$ - axis from some point to another is $8$, and then the area above the $x$ - axis again is $10$.

Step3: Calculate the net area

$\int_{0}^{a}f(x)dx=20 - 8+10$. $20-8 + 10=22$.

Answer:

$22$