I want to use a function as variable of integration for example in evaluating the integral:
$\int_0^1 e^{\cos x}f(\sin x)d\cos x$
in which $f(x)$ is an arbitrary function.
2026-03-27 08:49:34.1774601374
Numerically solve integral with a function as variable of integration
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To formalise the comments, you can take $y=\cos x$ so $d\cos x=dy$ and $\sin x = \sqrt{1-\cos^2x}=\sqrt{1-y^2}$ therefore your integral is $$\int_0^1 e^yf\left(\sqrt{1-y^2}\right)dy$$