Evaluate the following integrals as a limit of sums:

Formula used:

where,

Here, a = 0 and b = 2

Therefore,

Let,

Here, f(x) = 3x² – 2 and a = 0

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

f(0) = 3(0)² – 2 = 0 – 2 = -2

f(h)

= 3(h)² – 2

Similarly, f(2h)

= 3(2h)² – 2

Since -2 is repeating n times in series

Now take 3h² common in remaining series

Put,

Since,