Unit 5: Calculus
Topic 5.5: Introduction to Integration Questions
Practice 16 exam-style questions for IB Math AA SL Topic 5.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Evaluate2 marks
2026• Aimnova practice — 5.5.2
Evaluate ∫₁⁴ (2x + 1) dx.
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2026• Aimnova practice — 5.5.1
Find ∫(5 − 2x) dx.
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2026• Aimnova practice — 5.5.2
Evaluate ∫₀² (3x²) dx.
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2026• Aimnova practice — 5.5.2
Find the area enclosed by y = 3x², the x-axis, and the lines x = 0 and x = 2.
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2026• Aimnova practice — 5.5.1
A curve has f'(x) = 6x² − 4 and a stationary point — wait, instead: f'(x) = 6x² − 4 and f(0) = 7. Find f(x).
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2026• Aimnova practice — 5.5.1
Find ∫(8x³ − 6x + 1) dx.
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2026• Aimnova practice — 5.5.1
Find ∫(x² − 4/x²) dx.
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2026• Aimnova practice — 5.5.2
Find the area under the curve y = x² between x = 1 and x = 3.
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2026• Aimnova practice — 5.5.2
Evaluate ∫₁² (6x² − 2x) dx.
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2026• Aimnova practice — 5.5.2
Evaluate ∫₀³ (x² + 1) dx, then state what region this gives the area of.
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2026• Aimnova practice — 5.5.2
The area under y = x² + 2 from x = 1 to x = a is 14/3 + ... — instead: The region under y = x² between x = 0 and x = a has area 9. Find a.
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2026• Aimnova practice — 5.5.1
Find ∫6√x dx.
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2026• Aimnova practice — 5.5.1
Find ∫(3/x²) dx.
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2026• Aimnova practice — 5.5.2
The area under y = 4x from x = 0 to x = k is 50. Find k (k > 0).
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2026• Aimnova practice — 5.5.1
A curve has f'(x) = 4x − 3 and passes through (2, 5). Find f(x).
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2026• Aimnova practice — 5.5.1
The gradient of a curve is dy/dx = 3x² + 2x and the curve passes through the origin. Find y.
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