Question

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

Answer 1

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.