Find the integral of 3 4 cos ⁡ ( 2 t + 2 ) with respect to t.

Question

Find the integral of       3    4        ﻿    cos  ⁡  (  2  t  +  2  ) with respect to t.

Brianna Sims · Accepted Answer

Since       3    4   is constant with respect to t, move       3    4   out of the integral.      3    4    ∫  cos  ⁡  (  2  t  +  2  )  d  tLet u=2t+2. Then du=2dt, so       1    2    d  u  =  d  t. Rewrite using u and du.      3    4    ∫  cos  ⁡  (  u  )      1    2    d  uCombine   cos  ⁡  (  u  ) and       1    2  .      3    4    ∫            cos      ⁡      (      u      )        2    d  uSince       1    2   is constant with respect to u, move       1    2   out of the integral.      3    4    (      1    2    ∫  cos  ⁡  (  u  )  d  u  )Simplify.      3    8    ∫  cos  ⁡  (  u  )  d  uThe integral of   cos  ⁡  (  u  ) with respect to u is   sin  ⁡  (  u  )      3    8    (  sin  ⁡  (  u  )  +  C  )Simplify.      3    8    sin  ⁡  (  u  )  +  CReplace all occurrences of u with 2t+2.      3    8    sin  ⁡  (  2  t  +  2  )  +  C

Find the integral of

Answered question

Answer & Explanation

New Questions in Calculus 1