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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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13 questions

SA-9709-P3-I36-G013 marksL1 FoundationCalculatorBy parts
Find ∫xe2x dx\displaystyle\int xe^{2x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-Q011 markL1 FoundationCalculatorChoosing u
To find ∫xcos⁡2x dx\displaystyle\int x\cos2x\,dx by parts, take u=u=
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-Q031 markL1 FoundationCalculatorChoosing u
For ∫x3ln⁡x dx\displaystyle\int x^3\ln x\,dx by parts, the best choice of uu is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0013 marksL2 StandardCalculatorBy parts
Find ∫xsin⁡x dx\displaystyle\int x\sin x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0023 marksL2 StandardCalculatorChoosing u
Find ∫ln⁡x dx\displaystyle\int\ln x\,dx, for x>0x>0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0133 marksL2 StandardCalculatorBy parts
Find ∫xex dx\displaystyle\int xe^x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0033 marksL3 ExamCalculatorChoosing u
Find ∫x2ln⁡x dx\displaystyle\int x^2\ln x\,dx, for x>0x>0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0044 marksL3 ExamCalculatorDefinite
Find the exact value of ∫01xe−x dx\displaystyle\int_0^1xe^{-x}\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0053 marksL3 ExamCalculatorDefinite
Find the exact value of ∫1eln⁡x dx\displaystyle\int_1^e\ln x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0145 marksL3 ExamCalculatorDefinite
Find the exact value of ∫1exln⁡x dx\displaystyle\int_1^e x\ln x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0154 marksL3 ExamCalculatorBy parts
Find ∫xcos⁡2x dx\displaystyle\int x\cos2x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-IN-0166 marksL4 ChallengingCalculatorDefinite
Find the exact value of ∫01x2ex dx\displaystyle\int_0^1x^2e^x\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P3-I36-0065 marksL5 ExtensionCalculatorBy parts
By integrating by parts twice, find ∫exsin⁡x dx\displaystyle\int e^x\sin x\,dx.

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Salam Academy Original Practice · Proposed mark scheme