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Integrate 2x sin⁡2x.(a) \(\frac{sin⁡2x}{2}\)+x cos⁡2x+C(b) \(\frac{sin⁡2x}{2}\)-cos⁡2x+C(c) \(\frac{cos⁡2x}{2}\)-x cos⁡2x+C(d) \(\frac{sin⁡2x}{2}\)-x cos⁡2x+CThe question was asked during an interview.The above asked question is from Integration by Parts in chapter Integrals of Mathematics – Class 12

Answer»

Right CHOICE is (d) \(\FRAC{sin⁡2x}{2}\)-X cos⁡2x+C

To explain: By using ∫ u.v DX=u∫ v dx-∫ u'(∫ v dx)

∫ x TANX dx=2x ∫ sin⁡2x dx-∫ (2x)’ ∫ sin⁡2x dx

=2x (-\(\frac{cos⁡2x}{2}\))+2\(\int \frac{cos⁡2x}{2}\) dx

=-xcos 2x+∫ cos⁡2x dx

=\(\frac{sin⁡2x}{2}\)-x cos⁡2x+C


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