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Question
Integrate the following with respect to x.
If f'(x) = `1/x` and f(1) = `pi/4`, then find f(x)
Solution
f'(x) = `1/x`
f(x) = `int "f'"(x) "d"x = int 1/x "d"x`
f(x) = log|x| + c
f(1) = `pi/4
⇒ `log|1| + "c" = pi/4`
⇒ 0 + c = `pi/4`
∴ c = ``pi/4`
∴ Required f(x) = `log|x| + pi/4`
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