Question

Find the area of the region between the x-axis and the graph of f(x) from a=-1, to b=2, if f (x)=e^2x+3

Answer 1

$S=\int_{-1}^2 (e^{2x}+3)dx=(\frac12e^{2x}+3x)|_{-1}^2=\frac12e^{4}+6-$$(\frac12e^{-2}-3)=\frac12(e^4-e^{-2})+9\approx 36.231$