Evaluate the following integrals as a limit of sums:
Formula used:
where,
Here, a = 1 and b = 3
Therefore,
Let,
Here, f(x) = 2x + 3 and a = 1
Now, By putting x = 1 in f(x) we get,
f(1) = 2(1) + 3 = 2 + 3 = 5
Similarly, f(1 + h)
= 2(1 + h) + 3
= 2 + 2h + 3
= 2h + 5
In this series, 5 is getting added n times
Now take 2h common in remaining series
Put,
Since,