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d-dx-2-x-e-t-2-dt-




Question Number 170255 by mathlove last updated on 19/May/22
(d/dx)[∫_2 ^x e^t^2  dt=?
$$\frac{{d}}{{dx}}\left[\int_{\mathrm{2}} ^{{x}} {e}^{{t}^{\mathrm{2}} } {dt}=?\right. \\ $$
Answered by floor(10²Eta[1]) last updated on 19/May/22
∫_2 ^x e^t^2  dt=F(x)−F(2)  (d/dx)∫_2 ^x e^t^2  dt=(d/dx)F(x)=f(x)=e^x^2
$$\int_{\mathrm{2}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\mathrm{F}\left(\mathrm{x}\right)−\mathrm{F}\left(\mathrm{2}\right) \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\int_{\mathrm{2}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{F}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \\ $$

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