CAIE IGCSE Additional Mathematics 14.11 Integrating Powers of x Question Bank

Practise integrating power expressions, applying limits and integrating twice from a second derivative with curve conditions.

Exam points

increase each power by one and divide by the new power, adding the constant c
evaluate an antiderivative at both limits before simplifying parameter expressions
integrate a second derivative twice and use both given conditions to find constants

[Maximum number: 3]

Find $\int\left(4x+5-\frac{1}{2x+3}\right)\,dx$ .

$2x^2+5x-\frac12\ln(2x+3)+c\text{ oe}$
B3.

B2 for $2x^2+5x-\frac12\ln(2x+3)$ , or $2x^2+5x-\frac12\ln 2x+3+c$ , or $2x^2+5x+k\ln(2x+3)+c$ with $k\neq0$ .

B1 for $2x^2+5x+\ldots+c$ , or $\ldots-\frac12\ln 2x+3$ , or $\ldots+k\ln(2x+3)$ with $k\neq0$ .

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14.11. Integrate powers of x question 1