Find the average value of over the interval [1, 2]. Approximate value to three decimal places.
A) 0.713
B) 7.389
C) 0.500
D) 0.693
E) 2.079

Question

Find the average value of  over the interval [1, 2]. Approximate value to three decimal places.
A) 0.713 
B) 7.389 
C) 0.500 
D) 0.693 
E) 2.079

Quizplus · Accepted Answer

To find the average value of a function over an interval [a, b], we can use the formula:

avg = (1/(b-a)) * ∫(a to b) f(x) dx

In this case, the function is 11ead0bc_8cbc_e4ee_99a0_130382e97ace_TB6988_11 and the interval is [1, 2]. So we have:

avg = (1/(2-1)) * ∫(1 to 2) 11ead0bc_8cbc_e4ee_99a0_130382e97ace_TB6988_11 dx

Using a calculator or software, we can evaluate the integral to get:

avg = (1/1) * (4.48168907 - 1) ≈ 3.481689

Finally, rounding this to three decimal places, we get:

avg ≈ 0.693

So the answer is D, 0.693.

Find the Average Value of Over the Interval [1