**Question:**Find an expression that gives the area of the shaded region.**Diagram Explanation:**The diagram illustrates two curves, labeled \(f(x)\) and \(g(x)\), plotted on a coordinate plane. The curves intersect at two points, denoted as \(a\) and \(b\) on the x-axis. The region between these two curves from \(a\) to \(b\) is shaded.**Options:**Select all that apply:A. \(\int_a^b (f(x) - g(x)) \, dx\)B. \(\int_a^b (g(x) - f(x)) \, dx\)C. \(\int_a^b |f(x) - g(x)| \, dx\)D. none of the above

Introduction: Integral calculus can be used to calculate the area between two curves, which is the region between two intersecting curves. When we are aware of the equation for two curves and the locations of their intersections, integration can be used to determine the area under the curves.The graph is given by, We have to find the integral that defines the area of the region. From the graph f(x)>g(x)⇔f(x)-g(x)>0 from x=a to the intersection point of the graphs f(x) and g(x)⇔f(x)-g(x)<0, and g(x)>f(x) from the intersection point of the graphs f(x) and g(x) to x=b. So, the area of the region is given by the integral ∫abf(x)-g(x)dx. Hence, option (C) is correct.