Integration (AS Unit 1: Pure Mathematics A) — WJEC A-Level Mathematics
Test yourself on Integration (AS Unit 1: Pure Mathematics A) with WJEC A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Integration (AS Unit 1: Pure Mathematics A) explained
The Fundamental Theorem of Calculus establishes the profound connection between differentiation and integration, proving that differentiation and integration are inverse processes.
Read the full explanation
If f(x) is a continuous function on [a, b] and F(x) is an antiderivative such that F'(x) = f(x), then the definite integral evaluates the net accumulated area under the curve between boundaries: ∫ₐᵇ f(x) dx = [F(x)]ₐᵇ = F(b) − F(a). Indefinite integration reverses differentiation to produce the general family of antiderivatives ∫ f(x) dx = F(x) + c, where c is an arbitrary constant of integration representing vertical translation. The constant c is uniquely determined when an initial condition or boundary coordinate (x₀, y₀) through which the solution curve passes is provided.
Your focus
- Explain the Fundamental Theorem of Calculus linking differentiation and integration as inverse processes.
- Evaluate indefinite integrals including the arbitrary constant of integration + c.
- Determine specific constants of integration from boundary and initial conditions.
Integration (AS Unit 1: Pure Mathematics A) exam tips
Marking Points
- integrating f(x) to find an antiderivative F(x) with constant of integration + c
- substituting given boundary coordinates (x₀, y₀) to calculate the value of c
- evaluating definite integrals using the evaluation formula F(b) − F(a)
Examiner Tips
- 💡Always write + c as soon as you remove the integral sign in an indefinite integral.
- 💡Substitute given coordinate conditions carefully to solve for the specific constant c.
Common Mistakes
- omitting the arbitrary constant of integration + c in indefinite integrals
- subtracting the limits in reverse order, writing F(a) − F(b) instead of F(b) − F(a)