Integration - Definite Integral

Integration - Definite Integral

TGM Original Questions

Evaluate each definite integral.

  1. \(\displaystyle\displaystyle\int_{0}^{3} x(x^{3}-2 x^{2}+3) \mathrm{d} x\)
  2. \(\displaystyle\displaystyle\int_{2}^{4} x^{2}(x-1)^{2} \mathrm{d} x\)
  3. \(\displaystyle\displaystyle\int_{1}^{5}\left(\frac{x^{4}-3 x}{x^{2}}\right) \mathrm{d} x\)
  4. \(\displaystyle\displaystyle\int_{3}^{7}\left(\frac{\sqrt{x}+4}{\sqrt{x}}\right) \mathrm{d} x\)

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Answer:(a) \(\dfrac{108}{5}\); (b) \(\dfrac{1456}{15}\); (c) \(\dfrac{124}{3}-3\ln5\); (d) \(4+8\sqrt7-8\sqrt3\)

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