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