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 Feb27 answered Integration by parts Feb27 asked How does the method of Lagrange multipliers fail (in classical field theories with local constraints)? Feb11 awarded Citizen Patrol Jan17 comment Is everything an expression? Jan12 comment Find the positive real number(s) $c$ such that the graphs of $y=x^c$ and $x=y^c$ intersect (somewhere) at an angle $\frac{\pi}{4}$ I forgot to say - your solution is superior since the final equation that needs solving is simpler. Jan12 revised Find the positive real number(s) $c$ such that the graphs of $y=x^c$ and $x=y^c$ intersect (somewhere) at an angle $\frac{\pi}{4}$ added second solution and some comments Jan12 comment Find the positive real number(s) $c$ such that the graphs of $y=x^c$ and $x=y^c$ intersect (somewhere) at an angle $\frac{\pi}{4}$ Your second solution (which is, of course, correct) comes from just swapping the curves, or equivalently $c \to 1/c$. In my solution (now updated) that comes from using $\pm\pi/4$. Jan12 awarded Editor Jan12 revised Find the positive real number(s) $c$ such that the graphs of $y=x^c$ and $x=y^c$ intersect (somewhere) at an angle $\frac{\pi}{4}$ added 48 characters in body Jan12 answered Find the positive real number(s) $c$ such that the graphs of $y=x^c$ and $x=y^c$ intersect (somewhere) at an angle $\frac{\pi}{4}$ Dec30 comment Books to learn physics, being a math major @becko - Any particular reason? Dec30 comment Books to learn physics, being a math major @timur - they are a little dated, but still more modern than most uni physics courses. It would be good for a math major to see and use index notation - too many have a unhealthy disrespect for it! I haven't read Thirring... Dec30 comment Books to learn physics, being a math major +1 for Arnold's Mathematical Methods of Classical Mechanics Dec30 answered Books to learn physics, being a math major Nov20 comment Evaluating the improper integral $\int\limits_{0}^{\infty} \frac{x^{a-1} - x^{b-1}}{1-x} \ dx$ The initial equation given for I(a) requires a pole prescription to be well defined. The second equation implicitly assumes that the Cauchy principle value was used in the definition of I(a). After that it's clear sailing... Oct19 awarded Supporter Oct17 awarded Teacher Oct17 answered Evaluating the improper integral $\int\limits_{0}^{\infty} \frac{x^{a-1} - x^{b-1}}{1-x} \ dx$