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stringsofphysics
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- integral from minus to plus infinity of tan^2 x
∫tan^2 x ( -infinity to +infinity)
If it's homework, and you would like help, we would like to help you with your homework in order to help you to learn; however, we don't want to just plain do it for you ##-## as @suremarc indicated, you should make and show an attempt ##-## and please use ##\mathrm {\LaTeX}## ##-## if it's not homework, please let us know ##-## your reply that included your saying "it appeared as part of a sum in quantum mechanics" leaves whether it's homework or not as something of a curiosity ##\dots##stringsofphysics said:Thank you for the reply, it appeared in a part of sum in quantum mechanics.
P.S. I am new to Physics forum. Sorry, not used to its norms
Thanks for inputs!
The integration of tan^2 x from - to + infinity represents the area under the curve of the function tan^2 x, from negative infinity to positive infinity.
The formula for integrating tan^2 x from - to + infinity is ∫tan^2 x dx = x - (1/3)tan^3 x + C.
Yes, the integration of tan^2 x from - to + infinity can be solved using the substitution method, where u = tan x and du = sec^2 x dx.
The integration of tan^2 x from - to + infinity is significant in calculus and mathematics as it involves finding the area under a curve, which has many real-world applications in fields such as physics, engineering, and economics.
The integration of tan^2 x from - to + infinity is a divergent integral, meaning that it does not have a finite value. This is because the function tan^2 x has vertical asymptotes at x = (2n + 1)π/2, where n is an integer, and the area under these asymptotes is infinite.