Solution Found!

Calculus / Calculus: Early Transcendentals 1 / Chapter 7.3 / Problem 55E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Change Question

Solution: Completing the square Evaluate the following

Chapter 4, Problem 55E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Completing the square Evaluate the following integrals.

\(\int_{1 / 2}^{(\sqrt{2}+3) /(2 \sqrt{2})} \frac{d x}{8 x^{2}-8 x+11}\)

Questions & Answers

QUESTION:

Completing the square Evaluate the following integrals.

\(\int_{1 / 2}^{(\sqrt{2}+3) /(2 \sqrt{2})} \frac{d x}{8 x^{2}-8 x+11}\)

ANSWER:

Step 1 of 4

In this problem we have to evaluate $\int\limits_{1/2}^{(\sqrt{2}+3)/(2\sqrt{2})}\frac{dx}{8{x}^{2}\ -\ 8x\ +\ 11}$

Consider $\int\limits_{1/2}^{(\sqrt{2}+3)/(2\sqrt{2})}\frac{dx}{8{x}^{2}\ -\ 8x\ +\ 11}$

We can rewrite $8{x}^{2}\ -\ 8x\ +\ 11$ as $(2\sqrt{2}\ x-\sqrt{2}{)}^{2}+9$

Thus $\int\limits_{1/2}^{(\sqrt{2}+3)/(2\sqrt{2})}\frac{dx}{8{x}^{2}\ -\ 8x\ +\ 11}=\ \int\limits_{1/2}^{(\sqrt{2}+3)/(2\sqrt{2})}\frac{dx}{(2\sqrt{2}\ x\ -\ \sqrt{2}{)}^{2}\ +\ 9}$ … (1)

Study Tools You Might Need

Chapter: 6 Problem: 6.6

Classical Mechanics 0
In many problems in the calculus of variations, you need to know the length ds of a short segment of a curve on a surface, as in the expression (6.1). Make a table giving the appropriate expressions for ds in the following eight situations: (a) A curve given by y = y(x) in a plane, (b) same but x = x

Chapter: 5 Problem: 2P

Organic Chemistry 7
Determine the degree of unsaturation for the hydrocarbons with the following molecular formulas: a. \(\mathrm{C}_{10} \mathrm{H}_{16}\) b. \(\mathrm{C}_{20} \mathrm{H}_{34}\) c. \(\mathrm{C}_{8} \mathrm{H}_{16}\) d. \(\mathrm{C}_{12} \mathrm{H}_{20}\) e. \(\mathrm{C}_{40} \mathrm{H}_{56}\)

Chapter: 9 Problem: 43AYU

Fundamentals of Statistics 4
Coefficient of Skewness Karl Pearson developed a measure that describes the skewness of a distribution, called the coefficient of skewness. The formula is The value of this measure generally lies between ?3 and +3. The closer the value lies to ?3, the more the distribution is skewed left. The

Chapter: 22 Problem: 22.32

University Physics with Modern Physics (1) 14
A very small object with mass 8.20 * 10-9 kg and positive charge 6.50 * 10-9 C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90 * 10-8 C>m2 . The object is initially 0.400 m from the sheet. What initial speed must the object ha

Chapter: 7 Problem: 10

Elementary Statistics: A Step by Step Approach 8th ed. 8
Educational Television In a sample of 200 people, 154 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. If the television company wanted to publicize the proportion of viewers, do you think it should us

Chapter: 14 Problem: 14.2

Organic Chemistry 3
The 1 H NMR spectrum of 1,2-dimethoxyethane (CH3OCH2CH2OCH3) recorded on a 300 MHz NMR spectrometer consists of signals at 1017 Hz and 1065 Hz downfi eld from TMS. (a) Calculate the chemical shift of each absorption. (b) At what frequency would each absorption occur if the spectrum were recorded on a

Chapter: 7 Problem: 7

Urban Economics 8
Using Figure 177 as a starting point, suppose the initial utility-maximizing spending on special education is $5 rather than $25. As before, the lump-sum conditional grant for special education is $20. The income elasticity of demand for special education is 1.0. a. Show the response of the median ho

Chapter: 11 Problem: 11.11

Chemistry for today : general, organic, and biochemistry 9
Explain why the rate of chemical reactions is generally slow for organic compounds and usually fast for inorganic compounds.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account