Say $T(b)=\int_0^{10}f(b,x)dx$. I want to find the value of $b$ which minimises $T$ but evaluating that integral is quite difficult. If $f(b,x)$ was squared, however, it would be easier. So my question is are the stationary points for $\int_0^{10}f(b,x)dx$ the same as for $\int_0^{10}[f(b,x)]^2dx$? $f$ will be something of the form of $\sqrt{\frac{1+[-\frac{b+1}{5}x+b]^2}{-\frac{b+1}{10}x^2+bx}}$.
2026-02-23 12:49:13.1771850953
Are stationary points preserved when squaring a function under an integral?
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