Unit 5: Calculus
Topic 5.16: Integration by parts (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.16. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
For a definite integral, after substituting u you should:
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In LIATE, which factor should be u in ∫ x³ ln x dx?
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Show that by differentiating the right-hand side.
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Integration by parts comes from reversing which rule?
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To integrate ∫ 5(5x − 1)³ dx, the substitution u = 5x − 1 gives:
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After u = x² + 1 in ∫₀¹ 2x(x² + 1)⁵ dx, the integral becomes:
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Which integral is set up for u = cos x (du = −sin x dx)?
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If after one round of parts the new integral looks HARDER, you should:
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2026
How many applications of parts does ∫ x³ ex dx need?
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