WAEC 2022 · Paper 1 · Q34

Integration

The gradient of a function at any point $(x, y)$ is $2x - 6$ . If the function passes through $(1, 2)$ , find the function.

Worked solution (try it first)

Integrate the gradient: $y = \displaystyle\int (2x - 6)\,dx$
$= x^2 - 6x + c$ .
The curve passes through $(1, 2)$ : $2 = 1 - 6 + c$ , so $2 = -5 + c$ .
Add 5 to both sides: $c = 7$ , so $y = x^2 - 6x + 7$ , option D.

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