Integration — IGCSE Mathematics - Additional (0606) questions by topic
Integration in Additional Mathematics asks you to find the area enclosed between a curve and a tangent line, work out a definite integral such as the integral of sine from 0 to pi, and find the area bounded by a line segment joining two points on a curve and the curve itself. Find and show are the only command words tested, but each expects a fully worked, exact solution rather than a numerical approximation.
This is a small set of 5 real questions worth between 5 and 11 marks, all from 2025 papers. Because a single sign error or wrong limit substituted early on can undo an otherwise correct method, submit each worked solution for instant marking to check every line of integration and substitution before moving to the next question.
May–June 2025, Paper 11
The point A with x-coordinate 2 lies on the curve y = sqrt(4x + 1). The diagram shows part of this curve and the tangent to the curve at A. Find the area of the shaded region…
Answer this question and get it marked →May–June 2025, Paper 12
Find the integral from 0 to pi of sin(theta) d(theta).
Answer this question and get it marked →A curve is such that its gradient at the point (x, y) is given by (5x - 2)^(1/3). The curve passes through the point (2, 32/5). Find the coordinates of the stationary point on the…
Answer this question and get it marked →May–June 2025, Paper 13
The diagram shows part of the curve y = 3 / (x + 1) - (x - 2) / x. The points A and B lie on the curve such that the x-coordinate of A is 1 and the x-coordinate of B is 2. A line…
Answer this question and get it marked →May–June 2025, Paper 22
The diagram shows part of the curve y = 15/x - 5/x^2. The curve meets the x-axis at the point A. The curve has a maximum at the point B. Find the area of the shaded region…
Answer this question and get it marked →