Answer to Question #201518 in Calculus for Dhruv rawat

Question #201518

e^x

d/dx [ ∫ ( Int dt] = x- In 2

2

True or false with full explanation


1
Expert's answer
2021-06-13T16:10:49-0400

Let us find


"\\frac{d}{dx} [ \\int_2^{e^x}\\ln t\\ dt] =|u=\\ln t, dv=dt,du=\\frac{dt}{t},v=t|=\n\\frac{d}{dx} [t\\ln t|_2^{e^x}- \\int_2^{e^x} dt]= \n\\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


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