Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

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

$$\int_{\mathrm{2}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\mathrm{F}\left(\mathrm{x}\right)−\mathrm{F}\left(\mathrm{2}\right) \\ $$$$\frac{\mathrm{d}}{\mathrm{dx}}\int_{\mathrm{2}} ^{\mathrm{x}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}=\frac{\mathrm{d}}{\mathrm{dx}}\mathrm{F}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com