Evaluate the following integrals as a limit of sums:
Formula used:
where,
Here, a = 0 and b = 2
Therefore,
Let,
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)
Now take h2 and h common in remaining series
Put,
Since,