Evaluate the following integrals as a limit of sums:
Formula used:
where,
Here, a = 0 and b = 2
Therefore,
Let,
Here, f(x) = x2 + 1 and a = 0
Now, By putting x = 0 in f(x) we get,
f(0) = 02 + 1 = 0 + 1 = 1
Similarly, f(h) = h2 + 1
In this series, 1 is getting added n times
Now take h2 common in remaining series
Put,
Since,