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juantheron
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$\displaystyle (1)\;\; \int_{-\infty}^{\infty}\frac{x^2}{1+4x+3x^2-4x^3-2x^4+2x^5+x^6}dx$
MHB Integral from negative infinity to infinity
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The integral from negative infinity to infinity of the function $\frac{x^2}{1+4x+3x^2-4x^3-2x^4+2x^5+x^6}$ evaluates to $\pi$. This result is significant in the context of complex analysis and residue theory, where such integrals often arise in evaluating contour integrals. The polynomial in the denominator can be analyzed for its roots to determine the behavior of the integrand. The discussion emphasizes the importance of understanding the properties of the function and the application of integration techniques. This integral exemplifies how advanced calculus can yield elegant results in mathematical analysis.
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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