Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 0 and b = 2


Therefore,




Let,



Here, f(x) = x2 + 2 and a = 0




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


f(0) = (0)2 + 2 = 0 + 2 = 2


f(h)


= (h)2 + 2


Similarly, f(2h)


= (2h)2 + 2




Since 2 is repeating n times in series




Now take h2 common in remaining series





Put,



Since,
















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