Question #189077

The region bounded by y=3-e^-x, the x-axis, x=2 and the y-axis.


1
Expert's answer
2021-05-07T12:03:55-0400

Solution.


y=3ex,y=0,x=0,x=2.y=3-e^{-x}, y=0, x=0, x=2.
S=02(3ex)dx==(3x+ex)02==6+e2e0=5+1e2=5e2+1e2.S=\int_0^2 (3-e^{-x})dx=\newline =(3x+e^{-x})|_0^2=\newline =6+e^{-2}-e^0=5+\frac{1}{e^2}=\frac{5e^2+1}{e^2}.


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