>be Brahmin girl in Pune.>enslaved, trafficking, sold off at age 12>kotha training arc: dance, music, poetry, and milkin Musaal 24x7>convert to Islam, become Mubarak Begum>you cant enter Delhi without paying cumtax to her>breed by David Ochterlony, British Resident, 13 wives, sex addict>hosts last great gangbang at Delhi, Ghalib also joined>builds a mosque in Hauz Qazi, 1823>Now known worldwide as : "randi ki masjid">every Brahmin girl is still jealous of her
Gaussian integral
Consider
I = ∫[-∞ to ∞] e^(-x²) dx
Square it:
I² = ∫[-∞ to ∞] ∫[-∞ to ∞] e^(-x² + y²) dx dy
Switch to polar coordinates:
I² = ∫[0 to 2π] ∫[0 to ∞] e^(-r²) r dr dθ
Since
∫[0 to ∞] r e^(-r²) dr = ½,
we get
I² = 2π(½) = π.
Therefore,
∫[-∞ to ∞] e^(-x²) dx = √π
If a physical system has a continuous symmetry, then there is a corresponding conserved quantity.
Examples:
Time-translation symmetry ⟹ Conservation of energy
Space-translation symmetry ⟹ Conservation of momentum
Rotational symmetry ⟹ Conservation of angular momentum
In compact form:
Continuous symmetry ⟺ Conservation law
