CAIE IGCSE Additional Math 14.13 definite integrals and areas

Use this integrals-and-areas page to find intersections, split shaded regions and evaluate exact area expressions from diagrams.

Exam points

Find intersection points or limits before setting up the required area integral.
Use curve-minus-line or split-region methods for areas between curves and axes.
Evaluate exact definite integrals involving logarithms, powers or algebraic curves.

[Maximum number: 2]

The equation of a curve is $y=kxe^{-2x}$ , where k is a constant.

Find the exact value of $\int_0^1 4xe^{-2x}\,dx$ .

$-2e^{-2}-e^{-2}-(0-e^0)$
M1
$1-\frac{3}{e^2}$
or $1-3e^{-2}$
A1

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