Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 0 and b = 2


Therefore,




Let,



Here, f(x) = 3x2 – 2 and a = 0




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


f(0) = 3(0)2 – 2 = 0 – 2 = -2


f(h)


= 3(h)2 – 2


Similarly, f(2h)


= 3(2h)2 – 2




Since -2 is repeating n times in series




Now take 3h2 common in remaining series





Put,



Since,















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