The area of the bounded region.
The curves y=ex, y=e−x, x=−2, and x=1
Consider y1=ex, y2=e−x, x=−2, and x=1
Hence, use the formulae of A=∫abf(x)dx
Now according to the given expression, the value of the area bounded by the given curves from x=−2 to x=1
The region bounded by curves ∫−20(y2−y1) dx+∫01(y1−y2) dx
A=∫−20(y2−y1) dx+∫01(y1−y2) dx=∫−20(e−x−ex) dx+∫01(ex−e−x) dx=[−e−x−ex]−20+[ex+e−x]01=e2+e+1e+1e2−4
Conclusion: The value of the area bounded by these curves y1=ex, y2=e−x, x=−2, and x=1 is e2+e+1e+1e2−4.