query: How can I evaluate $\int_{-\infty}^{\infty} e^{-x^2} dx$ without using polar coordinates
positive_passages.docid: 4287
positive_passages.text: Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
negative_passages.docid: 41738
negative_passages.text: Best way to integrate $ \int_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $
negative_passages.docid: 98710
negative_passages.text: Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
negative_passages.docid: 29383
negative_passages.text: Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus
negative_passages.docid: 65407
negative_passages.text: Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
negative_passages.docid: 59667
negative_passages.text: Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
negative_passages.docid: 110922
negative_passages.text: What are different ways to compute $\int_{0}^{+\infty}\frac{\cos x}{a^2+x^2}dx$?
negative_passages.docid: 140638
negative_passages.text: Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
negative_passages.docid: 94395
negative_passages.text: Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
negative_passages.docid: 124445
negative_passages.text: Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
negative_passages.docid: 40881
negative_passages.text: Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
negative_passages.docid: 127711
negative_passages.text: Evaluating $\int_{0}^{1}\int_{0}^{1}\sqrt{x^{2}+y^{2}}dxdy$ using polar coordinates.
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
negative_passages.docid: 111775
negative_passages.text: $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
negative_passages.docid: 123694
negative_passages.text: How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
negative_passages.docid: 77834
negative_passages.text: Is it possible to compute $\int_{-\infty}^\infty {x \sin x\over x^4+1}dx$ without using complex analysis?