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juantheron
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$\displaystyle \int_{0}^{\frac{\pi}{2}}\sqrt{\sin x}dx.\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{\sin x}}dx =$
MHB Definite Integral $\sqrt{\sin x}$: Answers
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The discussion focuses on the evaluation of the definite integrals of $\sqrt{\sin x}$ and $\frac{1}{\sqrt{\sin x}$ from 0 to $\frac{\pi}{2}$. It highlights the use of Beta and Gamma functions to derive the results, with the first integral equating to (1/2)*Beta(3/4; 1/2) and the second to (1/2)*Beta(1/4; 1/2). The product of these two integrals is noted to equal pi. This demonstrates the interconnectedness of these mathematical functions in solving definite integrals. The discussion emphasizes the significance of Beta and Gamma functions in integral calculus.
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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