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