Step 1:
write the function
[tex]f(x)=x^2\text{ + 1}[/tex]
Step 2
split the range in three identical invervals of size
[tex]\begin{gathered} =\text{ }\frac{6\text{ - 0}}{3} \\ =\text{ 2} \end{gathered}[/tex]
Step 3:
For the first rectangle , base = 2
[tex]\begin{gathered} \text{Height = 2}^2\text{ + 1 = 4 + 1 = 5} \\ \text{Area = base }\times\text{ Height = 2 }\times\text{ 5 = 10} \end{gathered}[/tex]
Step 4:
For the second area
Base = 2
[tex]\begin{gathered} \text{Height is f(2+2) = f(4) = 4}^2\text{ + 1 = 16 + 1 = 17} \\ \text{Area = 2 }\times\text{ 17 = 34} \end{gathered}[/tex]
Step 5:
For the the third rectangle
Base = 2
[tex]\begin{gathered} \text{Height is f(4 + 2) = }6^2\text{ + 1 = 36 + 1 = 37} \\ \text{Area = 2 }\times\text{ 37 = 74} \end{gathered}[/tex]
Total area = 10 + 34 + 74 = 118
Area under the curve = 118
