CAIE IGCSE Additional Math 14.10 integration as reverse differentiation

Use this reverse-differentiation page to adapt a previous derivative, handle constants and evaluate indefinite or definite integrals.

Exam points

Use a previous differentiation result to rewrite the integral in a solvable form.
Find antiderivatives for expressions such as xe^(4x), xcos x or chain-rule forms.
Apply limits or add the constant of integration according to the question type.

[Maximum number: 3]

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

Use your answer to part (a) to find $\int 4xe^{-2x}\,dx$ .

$-2xe^{-2x}-e^{-2x}+c$
B3
B2 for $-2xe^{-2x}-e^{-2x}$ , or $\int4xe^{-2x}\,dx=-2xe^{-2x}+\int2e^{-2x}\,dx$ .
B1 for using $kxe^{-2x}=\int(ke^{-2x}-2kxe^{-2x})\,dx$ or better.

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14.10. Understand integration as reverse differentiation question 1