Jan 1, 2017 · 3 I was reading up about the Weierstrass Substitution and don't understand what 'No generality is lost' means in this context. In integral calculus, the tangent half-angle substitution is a …

Jun 2, 2021 · What was the intuition behind the Weierstrass substitution? Ask Question Asked 4 years, 8 months ago Modified 4 years, 8 months ago

Feb 22, 2024 · One way to avoid this is to rewrite the squared sine and cosine as another linear trigonometric function, thanks to $$\cos (2x) = 1 - 2\sin^2 (x) = 2\cos^2 (x) -1.$$ Here is the reason …

Mar 23, 2021 · The Weierstrass substitution is always valid in whatever you're doing, be it integrating tricky trigonometric integrals or solving trig equations (eg the one you're solving).

The Weierstrass substitution is great for transforming complex trig integrals into simpler rational functions. Wikipedia suggests that it wasn't invented by Weierstrass, since Euler was already fam...

Dec 28, 2019 · Weierstrass substitution means the tangent half-angle substitution. I.e., a particular kind of substitution. It doesn't mean integration by any substitution.

May 18, 2015 · Definite integral of $$\int_0^ {2\pi} \frac {1} {2+\cos x}$$ without using improper integral, I want to solve this without having to use $-\infty$ and $\infty$ on the integrals limits. Is that possibl...

Feb 22, 2025 · This substitution is definitely used outside of calculus. It is a special case of what is called a rational parametrization of a curve. Applications in number theory include describing all …

Jan 11, 2024 · Does Weierstrass substitution work for different arguments in the trig functions?

Feb 1, 2017 · Integral using Weierstrass Substitution Ask Question Asked 9 years ago Modified 9 years ago