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Anit [1.1K]
3 years ago
5

Find the average value of f(x)=e2x over the interval [2, 4].

Mathematics
1 answer:
shusha [124]3 years ago
5 0
<h2>Option B is the correct answer.</h2>

Step-by-step 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=\frac{1}{2}\times \left [ e^{2x}\right ]^4_2\\\\\int_{2}^{4}e^{2x}dx=\frac{1}{2}\times(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.

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