Question 1

Express the limit as a definite integral on the given interval. lim n→[infinity] n xi ln(1 + xi2) Δx, [2, 7] i = 1

Question 2

Answer:

Explanation:

$Consider \ the \ following \ series$

$\lim_(n \to \infty) \sum \limits ^n_(i=1) x_i \ In ( 1+ x_i^2) \Delta x , [2,7]$

$Let's \ recall \ the \ explanation \ of$ d
efinite
$\ integral \ in \ terms \ of \ Riemann \ sum$

$\int^b_a \ f(x) \ dx = \lim_(n \to \infty) \sum \limits ^n_(i=1) \ f(x_i) \Delta x , \ where \ \Delta x = (b-a)/(n)$

$By \ efinition, \ the \ limit \ is \ then \ expressed \ as \ integral$

$\lim_(n \to \infty) \sum ^a_(i=1) \ x_i \ In (1+x_i^2) \Delta x = \int^7_2 xIn (1+x^2) \ dx$

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