Answer:
6
Step-by-step explanation:
A right Riemann sum approximates a definite integral as:
[tex]\int\limits^b_a {f(x)} \, dx \approx \sum\limits_{k=1}^{n}f(x_{k}) \Delta x \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]
The exact value of the definite integral can be found by taking the limit of the Riemann sum as n approaches infinity:
[tex]\int\limits^b_a {f(x)} \, dx = \lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]
Given that the sum is equal to 2 (n + 1) (3n + 2) / n², the exact value of the integral is:
lim(n→∞) 2 (n + 1) (3n + 2) / n²
lim(n→∞) 2 (3n² + 5n + 2) / n²
lim(n→∞) (6n² + 10n + 4) / n²
6
