I have nearly solved this question but I'm getting a different answer when substituting limits:

$∫_0^2 \left[\sin⁡(2x)+\sec^2 (\frac{x}{2})\right]\,dx $

integrated to: $-\frac{1}{2}\cos(2x)+2\tan(\frac{x}{2})+c$

substituting limits:


simplify: $-\frac{1}{2}\cos(4)+2\tan(1)+\frac{1}{2}$

For me this evaluates to $0.036128...$, but the solution is actually $3.94163$...

Is there something obvious I'm missing?

  • 1
    $\begingroup$ When you're doing a definite integral, the constant of integration cancels out. Also, is your calculator in the right mode? Degrees versus radians? $\endgroup$ May 22, 2018 at 17:32
  • $\begingroup$ Did you use degrees or radians?? $\endgroup$ May 22, 2018 at 17:32
  • $\begingroup$ Thanks. So is 0.036128 degrees equally correct? Also, does that mean the limits should be stated in radians? How would one know whether an integral should be reported in radians or degrees? $\endgroup$
    – Paddington
    May 23, 2018 at 11:52
  • $\begingroup$ Thanks again. I just found this guide which explains it nicely. $\endgroup$
    – Paddington
    May 23, 2018 at 12:01

1 Answer 1


Did you use Degrees or radians while calculating it, because it is correct for radians.


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