Question

what is the area of the region bounded below by y=e^x and above by y=4e^-x, for x is greater than or equal to zero?

Answer 1

first find the point at which the upper and lower boundaries intersect.
e^x=4 e^(-x)
x=ln(4)-x
2x=ln(4)
x=ln(2)
next integrate to find the area
integrate(4e^(-x)-e^x,{x,0,ln(2)})

Answer 2

thank you :)