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Problem 60 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 xe^{-x^2} \, dx $

Answer

$\frac{1}{2}\left(1-\frac{1}{e}\right)$

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Video Transcript

we know that t is gonna be negative x squared with the substitution, which means that de Axe is negative. DT over two acts. Once we take the derivative, which ones are limits of integration? Change from 012 negative zero scored, which is zero to negative one squared, which is negative one. Therefore, we now have the constant negative 1/2 on the outside and then we have limits from zero to negative one, as we just established. Take the integral is actually pretty simple because we know the integral of the tea is simply each the tea. Now, using the fundamental theme of calculus you can plug in okay, And we could leave this infected formers 1/2 times one minus won over E.