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Question
`int_1^(sqrt3)dx/(1+x^2) ` equals:
Options
`pi/3`
`(2pi)/3`
`pi/6`
`pi/12`
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Solution
`pi/12`
Explanation:
Let `I = int_1^sqrt3 dx/(1 + x^2) = [tan^-1 x]_1^sqrt3`
`= [tan^-1 sqrt3 - tan^-1 1]`
`= pi/3 - pi/4`
`= pi/12`
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