Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can I use change of variables to turn $\int_{3\pi/2}^{2\pi}\cos x\, dx$ into $\int_{0}^{\pi/2}\cos x\, dx$? Letting $x \mapsto x - 3\pi/2$ doesn't seem to work.

share|cite|improve this question
It is dangerous to make a substitution and keep the variable name. – André Nicolas Mar 18 '12 at 0:51
why do you even need to change variable in the first place. It is a simple integral – Siddhi V Iyer Mar 18 '12 at 2:48
up vote 2 down vote accepted

Try $u=2\pi-x$. The differential will change sign, but you’ll also have to turn the integral upside down.

share|cite|improve this answer

Simply you can't do any changes of variable to change the intervales, the primitive of $\cos x$ is $\sin x$ so why do you need this change of variable ! so

$$\int_{3\pi/2}^{2\pi}\cos x\, dx= [\sin x]_{3\pi/2}^{2\pi}=\sin 2\pi -\sin 3\pi/2 =0-(-1)=1$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.