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,













3