Integration of f(x) with respect to x where f(x) = 1(x−1/2)2+3/4 will be-
A
+ C
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B
+ C
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C
+ C
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D
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Solution
The correct option is A + C The given problem is in the form of 1x2+a2 and we can directly use the corresponding formula which is ∫1x2+a2dx = 1atan−1(xa) + C Here, instead of simply x we have (x - 1/2) and a2 is equal to 3/4. So the respective answer would be 2√3tan−1(x−1/2√32) + C or 2√3tan−1(2x−1√3) + C