Explained: "Evaluate the integral. ∫−76e−0.25xdx"

elchatosarapage

Answered question

2021-11-23

Evaluate the integral.

\int_{- 7}^{6} e^{- 0.25 x} d x

Coldst

Beginner2021-11-24Added 18 answers

Step 1
Evaluate the integral:

\int_{- 7}^{6} e^{- 0.25 x} d x = - \frac{1}{0.25} {[e^{- 0.25 x}]}_{- 7}^{6}

= - \frac{1}{0.25} [e^{- 0.25 \times 6} - e^{- 0.25 \times (- 7)}]

= 4 (e^{1.75} - e^{- 1.5})

\approx 22.126

Step 2
Thus, the integral equals 22.126.

Vaing1990

Beginner2021-11-25Added 16 answers

Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:

\int_{a}^{b} f (x) d x = F (x) ∣_{a}^{b} = F (b) - F (a)

Step 2: In this case,

f (x) = e^{- 0.25 x}

. Find its integral.

- 4 e^{- 0.25 x} ∣_{- 7}^{6}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(6)−F(−7):

- 4 e^{- 0.25 \times 6} - (- 4 e^{- 0.25 \times - 7})

Step 4: Simplify.

- 4 e^{- 1.5} + 4 e^{1.75}

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