Question

calculate the definite integral by referring to the figure with the indicated areas. area ( a = 1.214 ) area ( c = 5.76 ) area ( b = 2.44 ) area ( d = 1.774 ) ( int_{b}^{0} f(x) d x=square )

Explanation:

Step1: Recall the property of definite integral and area

The definite integral \(\int_{b}^{0}f(x)dx=\int_{b}^{c}f(x)dx+\int_{c}^{0}f(x)dx\). The area above the \(x -\)axis contributes positively and the area below the \(x -\)axis contributes negatively.

Step2: Analyze the regions

For \(\int_{b}^{c}f(x)dx\), the region \(B\) is below the \(x -\)axis, so \(\int_{b}^{c}f(x)dx=- \text{Area of }B\). For \(\int_{c}^{0}f(x)dx\), the region \(C\) is above the \(x -\)axis, so \(\int_{c}^{0}f(x)dx=\text{Area of }C\)

Step3: Calculate the integral

$$
LATEXBLOCK0
$$

Answer:

\(3.32\)