H2 Math - Integration

• Audi

  23 Jan 12, 17:54

  Can someone verify the answer for integrating cos^2 (2x) cos (3x)? I got 0.5 [1/3 sin 3x + 1/14 sin 7x + 1/2 sin x] + c

   

  The answer provided says 0.5 (1/3 sin 3x + 1/7 sin (7/2x) + sin (1/2 x)] + c.

   

  Basically i have the fraction of 1/2 outside the "sin" function. In the answer provided, the 1/2 appears to be inside the sin function, hence giving terms like sin (7/2 x) and sin (1/2x) whereas I got sin 7x and sin x respectively. Which is the right version?

• wee_ws

  23 Jan 12, 19:04

  Hi,

    Wolfram Integrator (at http://integrals.wolfram.com/index.jsp) gives

    1/4 sin x + 1/6 sin 3x + 1/28 sin 7x.

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  23 Jan 12, 19:09

  Hi,

    One may proceed via two methods when I discussed this question with my students.

    For method 1, we consider double angle formula on (cos 2x)^2 and then use the factor formula.

    For method 2, we apply the factor formula several times, starting with (cos 2x)(cos 3x).

    Thanks.

  Cheers,
  Wen Shih