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Question
`int_6^(2/3) (dx)/(4 + 9x^2)` equals
Options
`pi/6`
`pi/12`
`pi/24`
`pi/4`
MCQ
Solution
`pi/24`
Explanation:
`int_0^(2/3) (dx)/(4 + 9x^2) = 1/9 int_0^(2/3) (dx)/(4/9 + x^2)`
= `1/9 - 1/(2/3) (tan^-1(x/(2/3)))_0^(2/3)`
= `1/6 [tan^-1 (3x)/2]_0^(2/3)`
= `1/6 [tan^-1 1 - tan^-1 0]`
= `1/6[pi/4 - 0]`
= `pi/24`
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