Ivan Shishkin, Rye (1878)

Problems/Riemann integrationExerciseUnreviewed

Quick integrations by part (level 22)

by Sequoia·
20
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
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These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Compute the following integrals using one integration by part.

  1. ∫01x3ex2 dx.\displaystyle\int_0^{1}x^3e^{x^2}\,\mathrm{d}x. using xex2=(12ex2)′xe^{x^2}=\left(\frac12 e^{x^2}\right)'.

  2. ∫1eln⁡(u) dt.\displaystyle\int_1^{e}\ln(u)\,\mathrm{d}t. using 1=(x)′1=(x)'.

  3. ∫0π/2arctan⁡(t) dt\displaystyle\int_0^{\pi/2}\arctan(t)\,\mathrm{d}t using 1=(t)′1=(t)'.

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