What is the arclength of $f (x) = e^{x^{2} - x}$ $f(x)=e^(x^2-x)$ in the interval $[0, 15]$ $[0,15]$ ?

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Answer 1 · 2017-03-28T21:10:53

The general formula for Arc Length of a function of x is:

$L = int_a^bsqrt(1+(f'(x))^2)dx$

Given $f(x)=e^(x^2-x)$

Find the Arc Length in the interval $[0,15]$

Compute $f'(x)$

$f'(x) = (2x-1)e^(x^2-x)$

$(f'(x))^2=(4x^2-4x+1)e^(2x^2-2x)$

I used WolframAlpha to calculate this:

$L = int_0^15sqrt(1+(4x^2-4x+1)e^(2x^2-2x))dx~~1.59xx10^91$

What is the arclength of f(x)=e^(x^2-x) f(x)=ex2−xf(x)=e^(x^2-x) in the interval [0,15][0,15][0,15]?