# Integration in polar coordinates [closed]

I was wondering if this property of integration is held true in the polar coordinates

$$\int_a^b f(\theta)\,\mathrm{d}\theta = -\int_b^a f(\theta)\,\mathrm{d}\theta$$

## closed as off-topic by Saad, mrtaurho, Vinyl_cape_jawa, José Carlos Santos, Riccardo.AlestraMar 15 at 15:05

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• Yes, this is valid for any integral and does not depend on a geometric interpretation. – Bernard Feb 4 at 8:58
• You can replace $\theta$ with any variable you like, it doesn't make a difference. – Qi Zhu Feb 4 at 9:06
• What confused me is that in polar coordinates the limit of integration is in a loop but i think i got it now.. thank you – Naifqar Feb 4 at 9:13

Yes, this is valid for any integral. From the fundamental thereom of calculus: https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Corollary $$\int_a^b f(\theta)\,\mathrm{d}\theta = F(b) - F(a)$$ $$-\int_b^a f(\theta)\,\mathrm{d}\theta = -(F(a)-F(b))=F(b) - F(a)$$