MATH CALCULUS2 very hard question HELP OUT!

Question

Determine the area of the region bounded by

y = e ^x , y = xe^x and x = 0 .

Answer 1

e^x and xe^x interesect at x equals 1 so this is the upper limit of integration. The limits of integration are 0 and 1

∫₀¹ e^x-xe^x = 2e^x-xe^{x which we then evaluate at both 1 and 0 and subtract.}

(2e¹-1e¹)-(2e⁰-0e⁰) = e-2 which as a decimal should be approximately .7183

This is the area between the two curves between x=0 and x=1

Answer 2

The answer is the integral from 0 to 1 of e^x - xe^x

This integrates as 2e^x - e^x

I will leave it to you to evaluate at the limits of integration.