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Calculus Level 1

∫ 0 1 e − x d x \large \displaystyle\int _{ 0 }^{ 1 }{ { e }^{ -x }\, dx }

If the integral above is in the form of A − B e , A - \dfrac Be,

where A A and B B are positive integers, find A + B A+B .

Clarification : e e denotes Euler's constant


The answer is 2.

Hamza A by Hamza A , 19, USA

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1 solution

Marta Reece
Apr 28, 2017

∫ 0 1 e − x d x = − e − x ∣ 0 1 = − e − 1 + e 0 = 1 − 1 e \int _{ 0 }^{ 1 }{ { e }^{ -x }\, dx }=-e^{-x}|_0^1=-e^{-1}+e^0=1-\frac{1}{e}

1 + 1 = 2 1+1=\boxed{2}

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