First slide

Evaluation of definite integrals

Question

If $A (t) = \int_{- 1}^{t} e^{- | \times |} d x,$ then $lim_{t \to \infty} A (t)$ is equal to

Moderate

A

$2 - e^{- 1}$
B

$3 - e^{- 1}$
C

4
D

0

Solution

$A (t) = \int_{- 1}^{0} e^{x} d x + \int_{0}^{t} e^{- x} d x = 1 - e^{- 1} - (e^{- t} - 1)$
$lim_{t \to \infty} A (t) = 2 - e^{- 1}$

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