`g(x) = int_3^x(e^(t^2 - t))dt` Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

Part 1 of the Fundamental Theorem of Calculus states that for a continuous function `f`
`F'_a(x)=f(x),` where `F_a(x)=int_a^xf(t)dt.`

Here `f(t)=e^(t^2-t)` and `g(x)=F_3(x).`

Therefore

 

`g'(x)=F'_3(x)=f(x)=e^(x^2-x).`