Question

calculate the definite integral by referring to the figure with the indicated areas.
int_{c}^{0} f(x) d x
area ( a = 1.585 ) area ( c = 5.624 )
area ( b = 2.374 ) area ( d = 1.683 )
int_{c}^{0} f(x) d x=square

Explanation:

Step1: Use the property of definite integral

The definite integral \(\int_{c}^{0}f(x)dx\) can be evaluated based on the area above and below the \(x -\)axis. For a function \(y = f(x)\), \(\int_{a}^{b}f(x)dx\) is equal to the area above the \(x -\)axis minus the area below the \(x -\)axis. Here, when integrating from \(c\) to \(0\), the region is above the \(x -\)axis.

Step2: Calculate the value of the integral

We know that \(\int_{c}^{0}f(x)dx\) is equal to the area of the region between \(x = c\) and \(x = 0\). From the figure, this area is given as Area \(C\).

Answer:

\(5.624\)