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Question
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
Options
a + b
`(ax^2)/2 + bx`
`(ax^2)/2 + bx + c`
b
Solution
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to `underlinebb((ax^2)/2 + bx)`.
Explanation:
Given
`d/dx [f(x)]` = ax + b
By integrating both sides, we get
f(x) = `int (ax + b)dx`
`\implies` f(x) = `(ax^2)/2 + bx + c`
Now, f(0) = 0
∴ f(0) = 0 + 0 + c
`\implies` c = 0
Then, f(x) = `(ax^2)/2 + bx`.
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