According to the given graph, a and b (that are the limits of the integral) are 1 and 3 respectively, this is because the area under the curve is being evaluated from 1 to 3.
It means that a=1 and b=3.
f(x) is the function of which we are calculating the integral. That function is a linear function. We can find it by finding the equation of the line:
[tex]m=\frac{1-3}{3-1}=\frac{-2}{2}=-1[/tex][tex]y=-x+4[/tex]
It means that f(x)=-x+4.
The area can be found using the definite integral:
[tex]\begin{gathered} \int_1^3(-x+4)dx \\ -\frac{x^2}{2}+4x \\ (-\frac{3^2}{2}+4(3))-(-\frac{1^2}{2}+4(1)) \\ (-\frac{9}{2}+12)-(-\frac{1}{2}+4) \\ -\frac{9}{2}+\frac{1}{2}+12-4 \\ -4+12-4 \\ 4 \end{gathered}[/tex]
It means that the area=4.
