I am trying to do the following integral:(adsbygoogle = window.adsbygoogle || []).push({});

$$\int_{\pi f}^{3\pi f} dx \sqrt{\cos(x/f)}.$$

Wolfram alpha - http://www.wolframalpha.com/input/?i=integrate+(cos(x))^(1/2)+dx+from+x=pi+to+3pi gives me

$$\int_{\pi f}^{3\pi f} dx \sqrt{\cos(x/f)} = 4f E(2) = 2.39628f + 2.39628if,$$

where E is the elliptic function.

Mathematica also gives me the same answer. How can the integral of arealintegrand withreallimits be complex?

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# I Complex integral of a real integrand

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