Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 0 and b = 2


Therefore,




Let,



Here, f(x) = x2 + x and a = 0




Now, by putting x = 0 in f(x) we get,


f(0) = 02 + 0 = 0 + 0 = 0


f(h)


= (h)2 + (h)


= h2 + h


Similarly, f(2h)


= (2h)2 + (2h)




Now take h2 and h common in remaining series





Put,



Since,
















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