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  "body": "\n## Example\n\nThe [[improper integral|0VCTBJMEJF]] of $e^{-x}$ over $[0, \\infty)$ converges, and\n$$\\int_0^\\infty e^{-x} \\, dx = 1.$$\nFor $b \u003e 0$, [[the exponential formula|06D0EWR2DV]] with $c = -1$ gives $\\int_0^b e^{-x} \\, dx = 1 - e^{-b}$. This tends to $1$ as $b \\to \\infty$.\n\n## Remarks\n\nIt is the case $s = 1$ of the [[gamma function|0V3FZMVB4K]]: $\\Gamma(1) = 1$.\nMathlib states it as `integral_exp_neg_Ioi_zero`.\n\n## Explanations\n\n### L1 human\n\nThe region under $e^{-x}$ is infinitely long, but its area is finite.\nThe area is exactly $1$.\n",
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