How Can you factor 1/2 out of integral

ikramkeyslo4s

ikramkeyslo4s

Answered question

2022-03-27

How Can you factor 1/2 out of integral of cos2x?
cos2xdx
simplifies to
12cosudu
where u=2x
My Question is where does the 12 that is factored out come from?
It would make more sense for a factor of 1/2 to be extracted if the integral was:
cosx2dx

Answer & Explanation

Denise Daniel

Denise Daniel

Beginner2022-03-28Added 8 answers

When you do a u-substitution, you have to substitute for every x in the integral, including the dx. Starting from u=2x, you can differentiate both sides and get dudx=2. We rewrite this as 12du=dx.
Thus, when you substitute in the integral, you replace the 2x with a simple u, and you replace the dx with 12du. We write the 12 out in front of the integral, and then we proceed with our simpler integral in terms of u.

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