ANSWER
15 square unit.
EXPLANATION
Step 1:
Recall that the right endpoint Riemann sum for
[tex]\begin{gathered} ^{}\int ^b_af(x)dx\text{ is given by } \\ \frac{b-a}{n}\sum ^n_{k\mathop=1}f(a+\frac{b-a}{n}k) \end{gathered}[/tex]
Step 2:
Note, if f(x) is continuous, then:
[tex]\lim _{n\to\infty}\frac{b-a}{n}\sum ^n_{k\mathop{=}1}f(a+\frac{b-a}{n}k)\text{ = }^{}\int ^b_af(x)dx\text{ }[/tex]
Step 3:
Now, applying the limit of the Reimann sums to evaluate the integral:
[tex]^{}\int ^2_0(3x+3)dx\text{ }[/tex]
Please, carefully check my working:
Hence, using the concept of the definite integral, the total area between the graph of f(x) and the x-axis by taking the limit of the associated right Riemann sum is 15 square unit.
