#### To determine

**To find:**

The area of the bounded region.

#### Answer

e2+e+1e+1e2−4.

#### Explanation

**Given:**

The curves y=ex, y=e−x, x=−2, and x=1

**Formulae used:**

The A=∫abf(x)dx

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.