Integration of $\int \sin(x^{\circ}) \operatorname{d}x$. The '$x$' is ok but this confuses me by creating '$x^{\circ}$'.This is not the differential like to solve it by chain rule. I thought the answer could be '$-\cos x/x^{\circ}$' but not sure.
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$\begingroup$Let consider a change of variable
$$y=x\cdot \frac{\pi}{180} \implies dy=\frac{\pi}{180}dx$$
therefore
$$\int \sin x° \,dx=\frac{180}{\pi}\int \sin \left(\frac{180}{\pi}y\right) \,\,dy=-\cos\left(\frac{180}{\pi}y\right) +c=-\cos x° +c $$
$\endgroup$ $\begingroup$When talking about angles, $x^\circ$ is the same as $x\cdot\frac{\pi}{180}$. In fact, in at least one online graphing calculator that I know of, the symbol $^\circ$ isn't a function or anything, it is actually encoded as the constant $\frac{\pi}{180}$.
$\endgroup$ $\begingroup$$\displaystyle\int \sin(x°) \,dx=\int \sin(\frac{x\pi}{180}) \,dx=-\dfrac{\cos(\dfrac{x\pi}{180})}{\dfrac{\pi}{180}}+c$
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