Question

e^x

d/dx [ ∫ ( Int dt] = x- In 2

2

True or false with full explanation

Answer 1

Let us find

$\frac{d}{dx} [ \int_2^{e^x}\ln t\ dt] =|u=\ln t, dv=dt,du=\frac{dt}{t},v=t|= \frac{d}{dx} [t\ln t|_2^{e^x}- \int_2^{e^x} dt]= \frac{d}{dx} [x{e^x}-2\ln 2- e^x+2]=xe^x+e^x-e^x=xe^x\ne x-\ln 2.$

Answer: false