Answer:
Step-by-step explanation:
[tex]Consider \ the \ following \ series[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} x_i \ In ( 1+ x_i^2) \Delta x , [2,7][/tex]
[tex]Let's \ recall \ the \ explanation \ of[/tex] d[tex]efinite[/tex] [tex]\ integral \ in \ terms \ of \ Riemann \ sum[/tex]
[tex]\int^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(x_i) \Delta x , \ where \ \Delta x = \dfrac{b-a}{n}[/tex]
[tex]By \ efinition, \ the \ limit \ is \ then \ expressed \ as \ integral[/tex]
[tex]\lim_{n \to \infty} \sum ^a_{i=1} \ x_i \ In (1+x_i^2) \Delta x = \int^7_2 xIn (1+x^2) \ dx[/tex]
