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,