89.9k views
5 votes
Find the average value of f(x)=e2x over the interval [2, 4].

a. 1463.18

b. 731.59

c. 1517.78

d. 23.60

User Lope
by
6.5k points

1 Answer

5 votes

Option B is the correct answer.

Explanation:

We need to find average value of
e^(2x) in [2,4]

Area of
e^(2x) in [2,4] is given by


\int_(2)^(4)e^(2x)dx=(1)/(2)* \left [ e^(2x)\right ]^4_2\\\\\int_(2)^(4)e^(2x)dx=(1)/(2)*(e^8-e^4)=1463.18

Area of
e^(2x) in [2,4] = 1463.18

Difference = 4 - 2 = 2

Average value = Area of
e^(2x) in [2,4] ÷ Difference

Average value = 1463.18 ÷ 2

Average value = 731.59

Option B is the correct answer.

User Chris Midgley
by
6.4k points
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