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Question
`int_0^(2/3) dx/(4+9x^2)` equals:
Options
`pi/6`
`pi/12`
`pi/24`
`pi/4`
Solution
`pi/4`
Explanation:
Let `I = int_0^(2/3) dx/(4 + 9x^2)`
`= 1/9 int_0^(2/3) dx/(4/9 + x^2)`
`= 1/9 * 1/2 [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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