#### To determine

**To prove:**

the inequality ∫01excosx dx≤e−1.

#### Answer

We could prove that in the inequality ∫01excosx dx≤e−1, left-hand side is less than or equal to the right-hand side.

#### Explanation

**Given:**

∫01excosx dx≤e−1

**Formulae used:**

The relation of −1≤cosx≤1

Consider ∫01excosx dx≤e−1

Hence, use the formulae of −1≤cosx≤1

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

cosx≤1∫01excosx dx≤∫01exdx≤[ex]01≤e−1

**Conclusion:**

We could prove that in the inequality ∫01excosx dx≤e−1, left-hand side is less than or equal to the right-hand side.

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