Question

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4

Answer 1

Looks like

$\displaystyle g(x)=\int_4^xe^{2t^2-4t}\,\mathrm dt$

By the FTC,

$\dfrac{\mathrm dg}{\mathrm dx}=e^{2x^2-4x}\cdot\dfrac{\mathrm dx}{\mathrm dx}=e^{2x^2-4x}$