-0100 e x-x- d x-A- e 100-1-100B- e 100-1- e -1C- 100 e -1D- e -1-100

The correct option is C 100(e 1)We know that nbsp; x [x]={x} where {x} represents the fractional part of x. Fundamental period of {x} is 1 ∴ nbsp;∫_0^100e^ ...

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Standard XII

Chemistry

Significant Figures

∫0100 e x-[x]...

Question

$100 \int 0 e^{x - [x]} d x =$

\frac{e^{100} - 1}{100}

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\frac{e^{100} - 1}{e - 1}

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100 (e - 1)

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\frac{e - 1}{100}

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Solution

The correct option is C $100 (e - 1)$
We know that
$x - [x] = {x}$
where ${x}$ represents the fractional part of $x$ .
Fundamental period of ${x}$ is $1$
$∴ 100 \int 0 e^{x - [x]} d x = 100 \int_{0}^{1} e^{x} d x = 100 [e^{x}]_{0}^{1} = 100 (e - 1)$

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100∫0ex−[x]dx=

The correct option is C 100(e−1)We know that x−[x]={x} where {x} represents the fractional part of x. Fundamental period of {x} is 1 ∴100∫0ex−[x]dx=100∫10exdx=100[ex]10=100(e−1)

$100 \int 0 e^{x - [x]} d x =$

The correct option is C $100 (e - 1)$
We know that
$x - [x] = {x}$
where ${x}$ represents the fractional part of $x$ .
Fundamental period of ${x}$ is $1$
$∴ 100 \int 0 e^{x - [x]} d x = 100 \int_{0}^{1} e^{x} d x = 100 [e^{x}]_{0}^{1} = 100 (e - 1)$