Techniques of Integration - Integration by the Reverse Chain Rule

Techniques of Integration - Integration by the Reverse Chain Rule

IP 4

Evaluate the following.

  1. \(\int_{0}^{1} x e^{-x^{2}} \mathrm{d}x\)
  2. \(\int_{1}^{5} e^{x} \sec^{2}(e^{x}) \mathrm{d}x\)

Solution:

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Answer:(a) \((e-1)/(2e)\). (b) Diverges to \(+\infty\); no finite value.

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