Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 3 and b = 5


Therefore,




Let,



Here, f(x) = 2 – x and a = 3



Now, By putting x = 3 in f(x) we get,


f(3) = 2 – 3 = -1


Similarly, f(3 + h)


= 2 – (3 + h)


= 2 – 3 – h


= -1 – h



In this series, -1 is getting added n times



Now take -h common in remaining series





Put,



Since,












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