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JAMB 2002 · UME · Q46

Evaluate ∫sin⁡3x dx\displaystyle\int \sin3x\,dx.

Worked solution (try it first)
  1. sin⁡\sin integrates to −cos⁡-\cos.
  2. For sin⁡3x\sin3x, also divide by 3, the coefficient of xx.
  3. So ∫sin⁡3x dx=−13cos⁡3x+c\int \sin3x\,dx = -\frac13\cos3x + c, option B.

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