Evaluate the following definite integral:
$integral subscript 0 superscript 1 straight x space straight e to the power of straight x squared end exponent space dx$

Solution

Let I = $integral subscript 0 superscript 1 straight x. straight e to the power of straight x squared end exponent dx$
Put $straight x squared space equals space straight y semicolon space space space space space space space space space space therefore space 2 space straight x space dx space equals space dy space space space space space space space space space rightwards double arrow space space space straight x space dx space equals space 1 half dy$
When x = 0, y = 0
When x = 1, y = 1
$therefore space space space space space straight I space equals space 1 half integral subscript 0 superscript 1 straight e to the power of straight y space dy space equals space 1 half left square bracket straight e to the power of straight y right square bracket subscript 0 superscript 1 space equals space 1 half left parenthesis straight e to the power of 1 minus straight e to the power of 0 right parenthesis space equals space 1 half left parenthesis straight e minus 1 right parenthesis$

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Integrals

Evaluate the following definite integral:
$integral subscript 0 superscript 1 straight x space straight e to the power of straight x squared end exponent space dx$

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