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Mathematics • 6 hours ago

Definite Integral Property with Floor Function

Resolved

Your Query:

"How do we split ∫[0 to 3] [x^2] dx where [.] denotes greatest integer function? Should we take roots sqrt(1), sqrt(2), sqrt(3)...?"

Resolution by Prof. Jagdish Meghani: Voice Note Attached

Yes! Break the integral at the points where x^2 is an integer: x ∈ [0, 1) -> 0; [1, √2) -> 1; [√2, √3) -> 2; [√3, 2) -> 3; up to √9 = 3. Multiply each interval length by the integer floor value.

Chemistry • 1 day ago

Electrophilic Aromatic Substitution with -NHCOCH3 group

In Review

Your Query:

"Why does acetanilide give predominantly para-bromoacetanilide instead of ortho upon bromination in acetic acid?"

Resolution by Er. Mayank Sir:

Due to steric hindrance of the bulky acetamido group (-NHCOCH3), the electrophile Br+ prefers the unhindered para position over ortho.