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 9h asked Is the transformation between these two functions smooth? 21h revised Closed form of the integral added 253 characters in body 22h revised Closed form of the integral deleted 25 characters in body 22h answered Closed form of the integral 23h comment Closed form of the integral Why do you think the integral has a closed form? Where does it come from? ... Nov 22 answered Solving the integral $\int_{-1}^1 2\sqrt{2-2x^2}\,dx$ Nov 18 comment Calculate $\int_0^{2\pi}\int_0^b \frac{r}{a-r\cos \vartheta}dr\,d\vartheta$. Are we sure this integral actually converges? To me it seems to blow up quite badly. Nov 17 awarded Good Answer Nov 17 awarded Notable Question Nov 16 comment Improper integral:- Change of Variable. Yes. How does you prove the identity $\int_a^b f(x)\,\mathrm{d}x = \int_a^b f(a+b - x) \,\mathrm{d}x$? One way is to use the substitution $x \mapsto a + b - u$ which only makes sense mathematically when $a$ and $b$ are real numbers. Lets for simplicity sake say that $a=0$. Then $\int_0^a f(x) = \int_0^a f(a-x)$. Geometrically we now integrate backwards starting at $a$ and working backwards untill zero, this notion of backwardness (or symetry around $(a+b)/2$) loses all meaning when we include infinity. Nov 16 comment Improper integral:- Change of Variable. Do you want to know how to calculate this integral? (I have it in my notes) Or do you wonder why you can not always apply the $f(x) = f(a + b - x)$ property? The last follows from that you need to integrate over a finite interval to give meaning to reflection. Nov 5 comment figure out $\int_{-\pi}^{\pi}\frac{ab}{a^2\cos^2 t+b^2\sin^2 t}\,dt$ Duplicate${}{}{}$ Nov 4 awarded Yearling Nov 4 revised How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$ deleted 11 characters in body Nov 4 revised help solving “unsolvable” definite integral describing aerodynamic property deleted 17 characters in body Nov 4 revised help solving “unsolvable” definite integral describing aerodynamic property added 671 characters in body Nov 4 answered help solving “unsolvable” definite integral describing aerodynamic property Nov 4 comment How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$ Without starting a longer discussion on the topic, that is the goal a tleast. Oh and it is in norwegian, not german however the languages share many similarities ;) Google translate should do the trick, however mathematics is the same in any language. Nov 4 comment How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$ Always ;) I wrote a few pages on it here folk.ntnu.no/oistes/Diverse/Integral/Integral%20Kokeboken.pdf. Look at 87-88. The idea to note is that x^2 + 1/x^2 can be factorized, and this shows up in many many integrals. These "tricks" are onyl tricks when you see them once, after that they are tools you can employ yourself on tricky integrals. Nov 4 revised How to compute $\int_0^{+\infty} \frac{dt}{1+t^4} = \frac{\pi}{2\sqrt 2}.$ added 8 characters in body