Integration (A2 Unit 3: Pure Mathematics B) — WJEC A-Level Mathematics
Test yourself on Integration (A2 Unit 3: Pure Mathematics B) with WJEC A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Integration (A2 Unit 3: Pure Mathematics B) explained
Standard indefinite integrals reverse standard derivatives: ∫ e^(kx) dx = (1/k) e^(kx) + c; ∫ (1/x) dx = ln|x| + c for x ≠ 0; ∫ sin(kx) dx = −(1/k) cos(kx) + c; and ∫ cos(kx) dx = (1/k) sin(kx) + c.
Read the full explanation
Dividing by the linear coefficient k originates from reversing the chain rule. Absolute value brackets ln|x| ensure the logarithm is defined for negative domain values. Integration is a linear operator, allowing expressions containing sums and constant multiples to be integrated term by term. For example, ∫ (4e^(3x) − 2/x + 5 sin 2x) dx = (4/3)e^(3x) − 2 ln|x| − (5/2)cos 2x + c. Trigonometric angles must be in radians. The arbitrary constant of integration + c must always be included for indefinite integrals.
Your focus
- Integrate exponential, reciprocal, and trigonometric functions with linear arguments.
- Divide by the coefficient k when reversing the chain rule for linear composites.
- Include absolute value signs in logarithmic integrals ln|x| and manage integration constants.
Integration (A2 Unit 3: Pure Mathematics B) exam tips
Marking Points
- integrating exponential terms e^(kx), dividing by the linear coefficient k
- integrating 1/x to obtain ln|x|
- integrating sine and cosine terms with correct signs: ∫ sin(kx) dx = −(1/k) cos(kx)
- including the arbitrary constant of integration + c in indefinite integrals
Examiner Tips
- 💡Remember: integrating sine gives minus cosine; integrating cosine gives positive sine.
- 💡Divide by the linear coefficient k when integrating functions with arguments of the form kx.
Common Mistakes
- multiplying by the coefficient k instead of dividing, writing ∫ sin(2x) dx = −2 cos(2x)
- omitting the negative sign when integrating sine, confusing the integral of sine with the derivative of sine