Express the arc length s of y x 3 for 0 x 8 as an integral in two ways, using the parametrizations r 1 (t) (t, t 3 ) and r 2 (t) (t 3 , t 9 ) Do not evaluate the integrals, but use substitution to show that they yield the same result

Question: Express the arc length s of y = x 3 for 0 x 8 as an integral in two ways, using the parametrizations

Express the arc length s of y = x³for 0 ≤ x ≤ 8 as an integral in two ways, using the parametrizations r₁(t) =(t, t³) and r₂(t) = (t³, t⁹). Do not evaluate the integrals, but use substitution to show that they yield the same result.

Step by Step Solution

★★★★★

3.43 Rating (143 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For rt 1t we have rt 1 31 hence r t 1 914 For rt 11 we ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

The rigid bar is pinned at A and supported by two aluminum rods, each having a diameter of 1 in. and a modulus of elasticity E al = 10(10 3 ) ksi. If the bar is initially vertical, determine the...

Compute the trapezoidal approximation T5 to the arc length s of y = tan x over [0, /4].

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Before you begin this assignment, be sure you have read the UMUC Family Clinic Case Study below and your Week 1 and Week2 syllabus readings, which discuss EHR functionality and Process...

Mathematics 30-1: Unit 2 2 Lesson A - Assignment Booklet 1. If the point (x, - 5 ) is a point on the unit circle in Quadrant IV, then the 9 exact value of x is - 2 14 A. 9 2 14 B. 9 - 106 C. 9 106 D....

Answer this: Figure 3.2 shows some special angles in standard position with the indicated terminal sides. The degree and radian measures are also given. "E. Ta nibs I 90% = 7 120 = 4 135 = 150 = 6...

The following function is positive and negative on the given interval. f(x) = 5 - 5x2; [0,4] a. Sketch the function on the given interval. b. Approximate the net area bounded by the graph offend the...

COMM 215: BUSINESS STATISTICS REVIEW PROBLEMS 1 Descriptive Statistics 1. The listing below gives the service window of A&W: 4.91 0.85 0.52 2.51 1.92 2.66 1.94 5.19 2.33 3.51 2.95 2.62 service times...

CHAPTER 9 Hypothesis Tests CONTENTS 9.4 POPULATION MEAN: UNKNOWN One-Tailed Test Two-Tailed Test Summary and Practical Advice 9.5 POPULATION PROPORTION Summary 9.6 HYPOTHESIS TESTING AND DECISION...

2.7. Explicit Solutions to Dierential Equations 109 power (kw) 20 15 10 5 0 08:00 10:00 12:00 14:00 16:00 time 18:00 2.7 Explicit Solutions to Dierential Equations In the very rare case in which an...

The integration problem is often impossible to be handled by analytical methods (studied in mathematical analysis or calculus). In such cases we have to rely on approximating methods. Monte Carlo...

22. A linear equation for the trend in demand data was found to be YT = 1,524 + 5.2X, where X is the number of the month as designated in the table that follows. MONTH January February March April...

From the Recording Industry Association of AmericaWeb site, we obtained data on the number of albums sold, in millions, for the top recording artists (U.S. sales only) as of November 6, 2008. Those...

Solve the problem and show the steps: Lay out the magic word, 0 xDEADBEEF, in memory starting from location 0 x 4 0 0 0 0 0 , for a MIPS computer. How about for an x 8 6 computer? ( Hint: is MIPS...

Using the Internet, identify a number of unlawful and potentially unlawful areas of inquiry. P-9687

Solve the equation cot(2) = 1 , where 0

Find the rectangular equation of the curve x = 5 tan t, y = 5 sec? t, TT

Solve the equation: 3x + 4 = 8 - x.

In this module, you explored policies and practices used by organizations to protect information. There are a variety of policies that are intended to improve the security posture of an organization....

Exercise 5-11 Accounting for notes receivable LO 5-4 Poole Enterprises loaned $25,000 to Boyd Co. on September 1, 2014, for one year at 6 percent interest. Required Show the effects of the following...

29. Brown Company's bank statement for September 30 showed a cash balance of s1,350. The company's Cash account in its general ledger showed a $995 debit balance. The following information was also...