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Integration - Integration of Power Functions

Integration - Integration of Power Functions

TGM Original Questions
  1. Find \(\displaystyle\displaystyle\int \sqrt{4x - 2} \mathrm{d}x\) .
  2. Determine whether the following integral has a real value, explaining your answer: \(\displaystyle\displaystyle\int_{0}^{5} 15 \sqrt{4x - 2} \mathrm{d}x\) .

Solution:

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Answer:(a) \(\dfrac16(4x-2)^{3/2}+C\). (b) No real value: the integrand is not real on \([0,1/2)\).

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