#### To determine

**To prove:**

the inequality ∫011+e2x dx≥e−1.

#### Answer

We could prove that in the inequality, ∫011+e2x dx≥e−1, the left-hand side is greater than or equal to the right-hand side.

#### Explanation

**Given:**

∫011+e2x dx≥e−1

**Formulae used:** The relation of 1+e2x≥e2x

Consider ∫011+e2x dx≥e−1

Hence, use the formulae of 1+e2x≥e2x

Now according to the given expression, the value of the given expression is

∫011+e2x dx≥∫01exdx≥∫01exdx≥[ex]01≥e−1

**Conclusion:**

We could prove the inequality ∫011+e2x dx≥e−1