Evaluate x 2 + 16 dx using trigonometric substitution. Then use Exercise 31 to verify that

Question:

Evaluate ∫ √x²+ 16 dx using trigonometric substitution. Then use Exercise 31 to verify that your answer agrees with the answer in Example 3.

EXAMPLE 3 Hyperbolic Substitution Calculate x +16dx.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Dec 25, 2023 08:29 AM

See More Questions

Evaluate x 2 9 dx in two ways: using trigonometric substitution and using hyperbolic substitution. Then use Exercise 31 to verify that the two answers agree. Data From Exercise 31 Verify the...
The van der Waals equation of state, an approximate representation of the behavior of gases at high pressure, is given by Where a and b are constants having different values for different gases. (In...
The article Seismic Hazard in Greece Based on Different Strong Ground Motion Parameters (S. Koutrakis, G. Karakaisis, et al., Journal of Earthquake Engineering, 2002:75109) presents a study of...
Clark had brain surgery. Insurance will not pay for the surgery until the deductible of $1,000 is hit. Then Clark's coinsurance of 80% / 20% kicks in. Clark has an out-of-pocket maximum of $7,500....
Determine the income participation of Hassell and Lawson, according to each of the five assumptions as to income division listed in Exercise 12-3 if the years net income is $380,000.
In the United States, the population mean height for 10-year-old girls is 54.5 inches. Suppose a random sample of 15 10-year-old girls from Brazil is taken and that these girls had a sample mean...
A combination is an ordered arrangement of objects.
Journalize the following data taken from the payroll register of University Printing as of April 15, 20: Regular earnings.........$5,418.00 Overtime earnings.......... 824.00 Deductions: Federal...
Cost and sales information for the most recent fiscal year are shown below:
Bruin Corporation has been authorized to issue 5,000 shares of 12 percent noncumulative, nonparticipating preferred stock with a par value of $100 per share and 200,000 shares of common stock with a...
Show that 0 e x 2 e x for x 1 (Figure 12). Use the Comparison Test to show that 0 e x2 dx converges. It suffices (why?) to make the comparison for x 1 because -4 -3 -2 -1 1 y = elx -2 3 4
Find the derivative using either method of Example 8. (x) = x 3 x EXAMPLE 8 Differentiate (for x > 0): (a) f(x) = x and (b) g(x)=xsin.x
Lonergan, Inc., a calendar year S corporation in Athens, Georgia, had a balance in AAA of $200,000 and AEP of $110,000 on December 31, 2015. During 2016, Lonergan, Inc., distributes $140,000 to its...
Notation Using the weights (Ib) and highway fuel consumption amounts (mi/gal) of the 48 cars listed in Data Set 35 "Car Data" of Appendix B, we get this regression equation: = 58.9 - 0.00749x, where...
Week 11-Final Exam: Chapters 5-7 Question 15 of 30 -135 Current At in Ppm 06-20 10%.onthe 1110077 OORE Textbook and M DOLL F T 19 19 Q w A R T Y 3 . 9 4 S D 4 G H A L x N M Cu T
We have two samples: sample 1 n= 39 -X= 98.2 S= 15.9 sample 2 n=31 -X=119.2 S= 23.0 begin testing whether u1
Discuss charitable purpose trusts under Section 3(1), Charities Act 2011.
Amadeus Corporation is considering the issue of a new product to be added to its product mix. They hired you, a recent business graduate from MacEwan, for conducting the analysis. The production line...
The ground-state electron configurations listed here are incorrect. Explain what mistakes have been made in each and write the correct electron configurations. Al: 1s22s22p43s23p3 B: 1s22s22p5 F:...
Why is it important to understand the macro-environment when making decisions about an international retail venture?
An important question about many functions concerns the existence and location of fixed points. A fixed point of f is a value of x that satisfies the equation f(x) = x; it corresponds to a point at...
The elevation h (in feet above the ground) of a stone dropped from a height of 1000 ft is modeled by the equation h(t) = 1000 - 16t 2 , where t is measured in seconds and air resistance is neglected....
Evaluate the following limits. x3 x2 5x 3 5 3 lim x-1 x4 + 2x3 - x? - 4x - x 4x 2
A stock is expected to pay a dividend of $1.50 at the end of the year (i.e., D 1 = $1.50), and it should continue to grow at a constant rate of 10% a year. If its required return is 14%, what is the...
The Hobby Shop has a checking account with a ledger balance of $1,700. The firm has $2,400 in uncollected deposits and $4,200 in outstanding checks. What is the amount of the disbursement float on...
An investment will pay you $34,000 in 11 years. If the appropriate discount rate is 6.1 percent compounded daily, what is the present value? (Use 365 days a year. Do not round intermediate...

Evaluate x 2 + 16 dx using trigonometric substitution. Then use Exercise 31 to verify that

Question:

EXAMPLE 3 Hyperbolic Substitution Calculate •√ √x² +16dx.

Step by Step Answer:

Let x 4 tan 9 Then dx 4 sec 0 de and x 16 dx 16 sec 0 de 8 tan 0 sec 0 8 ...View the full answer

Calculus

Students also viewed these Mathematics questions