# What is the arclength of #f(x)=x^2e^x-xe^(x^2) # in the interval #[0,1]#?

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To find the arc length of ( f(x) = x^2e^x - xe^{x^2} ) in the interval ([0, 1]), you need to compute the integral of the square root of ( 1 + (f'(x))^2 ) over the given interval. Calculate ( f'(x) ), square it, add 1, take the square root, and then integrate the resulting expression over the interval ([0, 1]). This will give you the arc length of the curve.

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