Evaluate: ∫(x^2 + x + 2) dx for x ∈ [0,2]

Question

Evaluate: \(\int\limits_0^2 (x^2 + x + 2) dx\)

Answer 1

Let f(x) = x² + x + 2, for 0 ≤ x ≤ 2 

Here, a = 0, b = 2 

We divide the closed interval [0, 2] into n subintervals each of length h

So, h = (b - a)/n = (2 - 0)/n = 2/n 

nh = 2

By definition,