Prove the following:
$integral subscript 0 superscript 1 straight x space straight e to the power of straight x space dx space equals space 1$

Solution

Let I = $integral subscript 0 superscript 1 xe to the power of straight x space dx space equals space left square bracket straight x space straight e to the power of straight x right square bracket subscript 0 superscript 1 space minus space integral subscript 0 superscript 1 1. space straight e to the power of straight x dx$
$equals space left square bracket xe to the power of straight x right square bracket subscript 0 superscript 1 space minus space left square bracket straight e to the power of straight x right square bracket subscript 0 superscript 1 space equals space left parenthesis straight e minus 0 right parenthesis space minus space left parenthesis straight e minus straight e to the power of 0 right parenthesis space equals space straight e minus straight e plus 1 space equals space 1$

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Integrals

Prove the following:
$integral subscript 0 superscript 1 straight x space straight e to the power of straight x space dx space equals space 1$

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