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Question Number 154052 by mathdanisur last updated on 13/Sep/21

Prove without any software  ∫_( 2βˆ’(√3)) ^( 1)  e^(βˆ’x^2 )  dx < (𝛑/6)  and∫_( 1) ^( 2+(√3)) e^(βˆ’x^2 )  dx < (𝛑/6)

$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software} \\ $$ $$\underset{\:\mathrm{2}βˆ’\sqrt{\mathrm{3}}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{e}^{βˆ’\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:<\:\frac{\boldsymbol{\pi}}{\mathrm{6}}\:\:\mathrm{and}\underset{\:\mathrm{1}} {\overset{\:\mathrm{2}+\sqrt{\mathrm{3}}} {\int}}\mathrm{e}^{βˆ’\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:\mathrm{dx}\:<\:\frac{\boldsymbol{\pi}}{\mathrm{6}} \\ $$

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