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Question
Using second fundamental theorem, evaluate the following:
`int_(-1)^1 (2x + 3)/(x^2 + 3x + 7) "d"x`
Sum
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Solution
`int_(-1)^1 (2x + 3)/(x^2 + 3x + 7) "d"x = int_(-1)^1 ("d"(x^2 + 3x + 7))/(x^2 + 3x + 7)`
= `[log|x^2 + 3x + 7|]_(-1)^1`
= `log|1 + 3 + 7| - log|1 - 3 + 7|`
= `log 11 - log 5`
= `log [11/5]`
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