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Question
Evaluate the following definite integrals:
`int_3^4 (d"x)/(x^2 - 4)`
Solution
Let I = `int_3^4 (d"x)/(x^2 - 4)`
= `int_3^4 ("d"x)/(x^2 - 2^2)` ......`[because ("d"x)/(x^2 - 2^2) = 1/(2"a") log((x - "a")/(x "a"))]`
= `[1/(2(2)) log((x - 2)/(x + 2))]_3^4`
= `1/4[log(2/6) - log(1/5)]`
= `1/4[log(2/6 xx 5/1)]`
= `1/4 log (5/3)`
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