Evaluate the integral. \int_{-7}^{6}e^{-0.25x}dx

elchatosarapage

elchatosarapage

Answered question

2021-11-23

Evaluate the integral.
76e0.25xdx

Answer & Explanation

Coldst

Coldst

Beginner2021-11-24Added 18 answers

Step 1
Evaluate the integral:
76e0.25xdx=10.25[e0.25x]76
=10.25[e0.25×6e0.25×(7)]
=4(e1.75e1.5)
22.126
Step 2
Thus, the integral equals 22.126.
Vaing1990

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:
abf(x)dx=F(x)ab=F(b)F(a)
Step 2: In this case, f(x)=e0.25x. Find its integral.
4e0.25x76
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(6)−F(−7):
4e0.25×6(4e0.25×7)
Step 4: Simplify.
4e1.5+4e1.75

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