Get the solution to "Evaluate the integral. ∫0we−2a|t|dt"

Daniaal Sanchez

Answered question

2021-10-01

Evaluate the integral.

\int_{0}^{w} e^{- 2 a | t |} d t

hajavaF

Skilled2021-10-02Added 90 answers

Step 1
Given integral:

\int_{0}^{w} e^{- 2 a | t |} d t

Step 2
Now,
|t|=t for all

t \geq 0

So,

\int_{0}^{w} e^{- 2 a | t |} d t = \int_{0}^{w} e^{- 2 a t} d t

Use the common integral:

\int e^{a u} d u = \frac{e^{a u}}{a}

\int_{0}^{w} e^{- 2 a | t |} d t = \int_{0}^{w} e^{- 2 a t} d t

= {[\frac{e^{- 2 a t}}{- 2 a}]}_{0}^{w}

= [\frac{e^{- 2 a w}}{- 2 a} - \frac{e^{- 2 a \times 0}}{- 2 a}]

= [\frac{e^{- 2 a w}}{- 2 a} + \frac{1}{2 a}]

= \frac{1}{2 a} [- e^{- 2 a w} + 1]

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