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Question
If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is ______.
Options
x2 + 3 log | x | + 1
x2 + 3 log | x |
`2 - 3/x^2`
x2 + 3 log | x | – 4
Solution
If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is x2 + 3 log | x |.
Explanation:
Given,
`d/dx [f(x)] = 2x + 3/x`
On integrating both sides,
`int d/dx [f(x)]dx = int(2x + 3/x)dx`
`\implies` f(x) = `(2x^2)/2 + 3 log |x| + C`
= x2 + 3 log | x | + C
Given: f(1) = 1
∴ f(1) = (1)2 + 3 × log 1 + C
`\implies` 1 = 1 + 0 + C
`\implies` C = 0
∴ f(x) = x2 + 3 log | x |.
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