Question

Help. i forgot simple laws of calculus. what is (d/dx) integral of e^(t^2)dx from 0 to x..... if i phrased that weird group chat me

Answer 1

d/dx(integral (e^(t^2)dx)) [from 0 to x] = e^(t^2 ( because diffrentiotion of an integarl = orginal function

Answer 2

\[\text{Let } f(t)=e^{t^2} \text{ and } \dfrac{dF}{dx}=f.\]Therefore:\[\dfrac{d}{dx}\left[\int\limits_0^xe^{t^2}dt\right]=\dfrac{d}{dx}\left[\int\limits_0^x f dt\right]=\dfrac{d}{dx}\left[F(x)-F(0)\right]=\dfrac{d}{dx}F(x)=f(x)=e^{x^2}\]