Chapter 14: Q. 1TB (page 1105)

Average value: Review the average value formula from Section 4.6. Use the formula to compute the average value of the following functions.
$g (x) = x^{2} + x + 2 on [1, 5]$

Short Answer

Expert verified

The average value of the function is $15.33$ .

Step by step solution

Step 1. Given Information

We have to find the average value formula from Section 4.6. Use the formula to compute the average value of the following functions.

$g (x) = x^{2} + x + 2 on [1, 5]$

Step 2. The formula for the average value of a function A is A=1b-a∫abF(x)dx

$A = \frac{1}{5 - 1} \int_{1}^{5} (x^{2} + x + 2) d x A = \frac{1}{4} {[\int x^{2} d x + \int x d x + 2 \int d x]}_{1}^{5} A = \frac{1}{4} {[(\frac{x^{2 + 1}}{2 + 1}) + (\frac{x^{1 + 1}}{1 + 1}) + 2 x]}_{1}^{5} A = \frac{1}{4} {[(\frac{x^{3}}{3}) + (\frac{x^{2}}{2}) + 2 x]}_{1}^{5}$

Step 3. Now putting the value.

$A = \frac{1}{4} [(\frac{5^{3}}{3} + \frac{5^{2}}{2} + 2 \times 5) - (\frac{1^{3}}{3} + \frac{1^{2}}{2} + 2 \times 1)] A = \frac{1}{4} [(\frac{125}{3} + \frac{25}{2} + 10) - (\frac{1}{3} + \frac{1}{2} + 2)] A = \frac{1}{4} [(\frac{125}{3} \times \frac{2}{2} + \frac{25}{2} \times \frac{3}{3} + 10 \times \frac{6}{6}) - (\frac{1}{3} \times \frac{2}{2} + \frac{1}{2} \times \frac{3}{3} + 2 \times \frac{6}{6})] A = \frac{1}{4} [(\frac{250}{6} + \frac{75}{6} + \frac{60}{6}) - (\frac{2}{6} + \frac{3}{6} + \frac{12}{6})] A = \frac{1}{4} [(\frac{250 + 75 + 60}{6}) - (\frac{2 + 3 + 12}{6})] A = \frac{1}{4} [\frac{385}{6} - \frac{17}{6}] A = \frac{1}{4} [\frac{385 - 17}{6}] A = \frac{1}{4} \times \frac{368}{6} A = 15.33$

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Average value: Review the average value formula from Section 4.6. Use the formula to compute the average value of the following functions.
$g (x) = x^{2} + x + 2 on [1, 5]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The formula for the average value of a function A is A=1b-a∫abF(x)dx

Step 3. Now putting the value.

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Average value: Review the average value formula from Section 4.6. Use the formula to compute the average value of the following functions.g(x)=x2+x+2on[1,5]

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The formula for the average value of a function A is A=1b-a∫abF(x)dx

Step 3. Now putting the value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Average value: Review the average value formula from Section 4.6. Use the formula to compute the average value of the following functions.
$g (x) = x^{2} + x + 2 on [1, 5]$