Techniques of Integration - Integrating Powers of Sine and Cosine

Techniques of Integration - Integrating Powers of Sine and Cosine

Evaluate the following

  1. \(\displaystyle\displaystyle \displaystyle\int_{0}^{\frac{\pi}{4}} 3\cos 2x + 1 \, \mathrm{d}x\)
  1. \(\displaystyle\displaystyle \displaystyle\int_{0}^{\frac{\pi}{6}} 4\sin 3x + \cos^2 x \, \mathrm{d}x\)

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Answer:(a) \(\frac32+\frac\pi4\) (b) \(\frac43+\frac{\sqrt3}{8}+\frac\pi{12}\)

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