The value of -01 1 - e - xdx is equal to

The correct option is A 2 1/e ∫_0^1 (1+e^ x) dx ∫_0^1 dx + ∫_0^1 e^ xdx [x]_0^1 [e^ x]_0^1 [1 0] [e^ 1 1] ...

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Byju's Answer

Standard XII

Mathematics

Integration of Piecewise Continuous Functions

The value of ...

Question

The value of $\int_{0}^{1} (1 + e^{- x}) d x$ is equal to

2 - \frac{1}{e}

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2 + \frac{1}{e}

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e + \frac{1}{e}

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none of these

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Solution

The correct option is A $2 - \frac{1}{e}$
$\int_{0}^{1} (1 + e^{- x}) d x$
$\int_{0}^{1} d x$ + $\int_{0}^{1} e^{- x} d x$
$[x]_{0}^{1}$ - $[e^{- x}]_{0}^{1}$
$[1 - 0]$ - $[e^{- 1} - 1]$
$2 - e^{- 1}$

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The value of ∫10(1+e−x)dx is equal to

The correct option is A 2−1e∫10(1+e−x)dx∫10dx + ∫10e−xdx[x]10 - [e−x]10[1−0] - [e−1−1]2−e−1

The value of $\int_{0}^{1} (1 + e^{- x}) d x$ is equal to

The correct option is A $2 - \frac{1}{e}$
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$[x]_{0}^{1}$ - $[e^{- x}]_{0}^{1}$
$[1 - 0]$ - $[e^{- 1} - 1]$
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