Unit 5: Calculus
Topic 5.11: Definite Integration Questions
Practice 16 exam-style questions for IB Math AA SL Topic 5.11. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026• Aimnova practice — 5.11.1
Given ∫₀⁶ h(x) dx = 15, find ∫₆⁰ h(x) dx and ∫₆⁶ h(x) dx.
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2026• Aimnova practice — 5.11.1
Evaluate ∫₀π/2 sin x dx.
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2026• Aimnova practice — 5.11.1
Evaluate ∫₀¹ e3x dx, giving an exact answer.
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2026• Aimnova practice — 5.11.1
Given ∫₁⁴ f(x) dx = 10 and ∫₁⁷ f(x) dx = 26, find ∫₄⁷ f(x) dx.
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2026• Aimnova practice — 5.11.1
Evaluate ∫₁² (6x² − 4x + 1) dx.
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2026• Aimnova practice — 5.11.2
Find the area between the curve y = x² − 9 and the x-axis from x = 0 to x = 3.
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2026• Aimnova practice — 5.11.2
Find the area enclosed between y = 2x and y = x².
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2026• Aimnova practice — 5.11.2
The curve y = x² − 2x meets the x-axis at x = 0 and x = 2, dipping below it. Find the area between the curve and the x-axis on [0, 2].
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2026• Aimnova practice — 5.11.2
Find the area enclosed between y = 4x − x² and the x-axis.
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2026• Aimnova practice — 5.11.1
Water flows into a tank at a rate r(t) = 20 − 2t litres per minute. Find the volume added between t = 0 and t = 5.
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2026• Aimnova practice — 5.11.1
A quantity changes at rate dQ/dt = 5e−0.1t. Given Q = 100 at t = 0, find Q at t = 8 (3 s.f.).
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2026• Aimnova practice — 5.11.2
Using a calculator, find the area between y = eˣ and y = x + 1 from x = 0 to x = 1.
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2026• Aimnova practice — 5.11.1
A car decelerates with velocity v = 30 − 2t m/s. Find the distance travelled from t = 0 until it stops.
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2026• Aimnova practice — 5.11.2
Find the area between y = x² and y = 4 (the region enclosed by the curve and the line).
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2026• Aimnova practice — 5.11.2
Find the area enclosed between y = x³ and y = x (for x ≥ 0).
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2026• Aimnova practice — 5.11.2
Find the area between the curves y = x² and y = 2 − x² (the region they enclose).
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