CAIE A-Level Mathematics 1.8.2 Constant of Integration

Practise recovering a curve from its derivative, retaining + c and using a given point or stationary-point condition to determine the constant before finding further coordinates.

Exam points

integrate every derivative term and include + c before using any coordinate information
substitute the given point into the antiderivative and solve the resulting equation for c
use the completed curve equation to calculate another coordinate or verify a stated point

[Maximum number: 2]

The function f is defined by $\mathrm{f}(x)=\frac{2}{(x+2)^{2}}$ for x>-2.

The equation of a curve is such that $\frac{\mathrm{d} y}{\mathrm{~d} x}=\mathrm{f}(x)$ . It is given that the point (-1,-1) lies on the curve.

Find the equation of the curve.

-1=-2+c
M1
Substitute x=-1, y=-1 into their integrated expression ( c
present)
$y=\frac{-2}{x+2}+1$
A1
Accept $y=-2(x+2)^{-1}+1 .-2$ must be resolved.

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1.8.2—Constant of integration question 1