Free Integration & areas questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Integration & Areas worksheet →All Calculus questionsThe graphs of y = 0.5x3 and y = 2x + 1 intersect at two or more points.
Find the x-coordinates of the two leftmost points of intersection.
Find the area of the region enclosed between these points.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −1.68, −0.539 GDC (M1) −1.68, −0.539 A1 | 2 |
| (b) | 0.406 integral of the difference (M1) correct limits (A1) 0.406 A1 | 3 |
The gradient function of a curve is f′(x) = 3x2 − 4x + 3. The curve passes through the point (1, 3).
Find f(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| f(x) = x3 − 2x2 + 3x + 1 attempt to integrate (M1) x3 − 2x2 + 3x + C A2 substituting the point (M1) C = 1 A1 | 5 |
The graph of y = −2(x − 1)(x − 4) meets the x-axis at A and B.
Write down the x-coordinates of A and B.
Find the area enclosed by the graph and the x-axis.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 1, 4 x = 1, x = 4 A1 | 1 |
| (b) | 9.00 ∫14y dx (M1) correct limits and integrand (A1) 9.00 A1 | 3 |
The graphs of y = x2 − 2 and y = 2cos x intersect at two or more points.
Find the x-coordinates of the two leftmost points of intersection.
Find the area of the region enclosed between these points.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −1.48, 1.48 GDC (M1) −1.48, 1.48 A1 | 2 |
| (b) | 7.74 integral of the difference (M1) correct limits (A1) 7.74 A1 | 3 |
The gradient function of a curve is f′(x) = 3x2 − 4x + 5. The curve passes through the point (2, 5).
Find f(x).
| Part | Answer and marking points | Marks |
|---|---|---|
| f(x) = x3 − 2x2 + 5x − 5 attempt to integrate (M1) x3 − 2x2 + 5x + C A2 substituting the point (M1) C = −5 A1 | 5 |
The graph of y = −2(x − 1)(x − 6) meets the x-axis at A and B.
Write down the x-coordinates of A and B.
Find the area enclosed by the graph and the x-axis.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 1, 6 x = 1, x = 6 A1 | 1 |
| (b) | 41.7 ∫16y dx (M1) correct limits and integrand (A1) 41.7 A1 | 3 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in