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

Answer 1

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`.