Evaluate the following integral as a limit of sums: ∫ (x^2 - x)dx, x ∈ [0, 2]

Question

Evaluate the following integral as a limit of sums:

\(\int\limits_{0}^{2} \) (x² - x)dx

Answer 1

To find: \(\int\limits_{0}^{2} \) (x² - x)dx

Formula used:

where,

Here, f(x) = x² – x and a = 0

Now, by putting x = 0 in f(x) we get,

f(0) = 0² – 0 = 0 – 0 = 0

f(h) =

(h)² – (h)

= h² – h

Similarly, f(2h)

= (2h)² – (2h)

= (2h)² – 2h

Put,

h = \(\cfrac2n\)

Since,

Hence, the value of