IB Maths AI HL Ahl 5 12 Hl Areas and Volumes Questions

Practise finding areas between curves and volumes of revolution with correct bounds, then interpreting signed integrals, units and the contextual result.

Exam points

Find areas enclosed by curves and coordinate axes, splitting regions and handling signed integrals.
Calculate volumes of revolution about the x- or y-axis using the appropriate radius and bounds.
Interpret area/volume results in context with correct units and justify the limits.

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Study AHL 5.12 (HL)—Areas and volumes conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Hence find the area bounded by the x-axis, the curve $\mathrm{y}=x e^{-x^{2}}$ and the line x=k. Give your answer in terms of k.

Recognition that 0 is the lower limit and substitute both 0 and k into the previous expression.

\int_0^k xe^{-x^2}\,dx=\left[-\frac12e^{-x^2}\right]_0^k=\frac12-\frac12e^{-k^2}

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IB Maths AI HL Ahl 5 12 Hl Areas and Volumes Questions question 1