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