Q. 65.0( 1 Vote )

Evaluate the following integrals as a limit of sums:


Answer :


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,













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