If n is a positive integer, prove that 1 0 (ln x) n dx (1) n n ...

n is a positive integer so Thus by repeated application of lHospita ...

If n is a positive integer, prove that 1 0 (ln x) n dx = (1)

Question:

If n is a positive integer, prove that ∫¹₀ (ln x)ⁿ dx = (–1)ⁿn!.

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

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

See More Books

Question Posted: Jan 13, 2021 05:56 AM

See More Questions

Is this proof that whenever n is a positive integer, correct? Justify your answer. Basis step: The result is true when n = 1 because Inductive step: Assume that the result is true for n. Then Hence,...
If n is a positive integer, show that
If n is a positive integer, show that
On July 7, Splish Ltd. purchased 1,100 common shares in a privately-owned company named TWR Ltd. As the TWR shares were not traded on any stock exchange, Splish elected to account for the investment...
Jacobi's method for a symmetric matrix A is described by A1 = A, A2 = P1A1Pt1 and, in general, Ai+1 = PiAiPti. The matrix Ai+1 tends to a diagonal matrix, where Pi is a rotation matrix chosen to...
Imagine that you are a hacker and have developed a Trojan horse program. What tactics might you use to get unsuspecting victims to load the program onto their computer?
On June 8, 2017, Eugene Weiner made a post on Isaac Aflalos Facebook page. The post read, Yurim and Isaac took advantage of a old 94plus sick man elder abuse [sic]. Alflalo took umbrage to the post...
AMR Corporation (parent company of American Airlines) reported the following for 2011 (in millions). Service cost .......... $366 Interest on P.B.O. ........ 737 Return on plan assets ...... 593...
Commencing 1 April 2022, Morgan Landscaping Pty Ltd (morgan) provided Larissa (an employee) with the use of a Volkswagen Golf car. The car cost $55,000 (including GST) and was used privately every...
Company ABC is a multinational company in Australia which has its branches all over the world. It has few servers like database server, Web server, Mail server and Storage Devices and different...
Evaluate the integral. 0 sin 2 t cos 4 t dt
Use (a) The Trapezoidal Rule (b) The Midpoint Rule (c) Simpsons Rule to approximate the given integral with the specified value of n. - x dx, n = 10 Jo
Evaluate the following integrals using the Fundamental Theorem of Calculus. 0 7/4 sec- d
Construct a 95 % confidence interval for the mean home price. What happens to the size of the confidence interval?
Suppose X has an exponential distribution with = 1/3 . Find the following probabilities: (a) P(3 < X < 5) (b) P(5 X 10) (c) P(2 < X < 1)
Go to the St. Louis Federal Reserve FRED database and find data on the net saving rate as a percentage of national income (W207RC1A156NBEA). a) Calculate the average net saving rate over the period...
Suppose X has an exponential distribution with = 4. Find the following probabilities: VI VI VI (a) P(X .3) (b) P(X < .5) (c) P(X 1.6)
A bank manager finds from reviewing her records that the amount of money deposited on Saturday morning is normally distributed with a standard deviation of $150. A random sample of 7 customers...
Explain the relationship between the learning curve and a firm's cost function. Would economists consider the learning curve a short-run or a long-run phenomenon?
Archangel Corporation prepared the following variance report. Instructions Fill in the appropriate amounts or letters for the question marks in the report. ARCHANGEL CORPORATION Variance...
Show that the function is differentiable by finding values of 1 and 2 that satisfy Definition 7. f (x, y) = xy - 5y 2
Use the Chain Rule to find dz/dt or dw/dt. z = x - y/x + 2y, x = e t , y = e - t-
Use the Chain Rule to find z/s and z/t. z = e r cos , r = st, = s 2 + t 2
What is the ranking of airlines from highest to lowest in terms of total revenue in 2018? Is there a correlation between unearned revenue to total revenue ratio and total revenue in 2018?
Exercise1 (20 points) Background readings Chapter 4 Scenario1 Consider an individual who has a 2-year undergraduate Diploma in Business and has a $30,000/year wage profile over his life cycle. Now,...
Case Study about SAN MIGUEL CORPORATION , following this format. And include all the references. Title Executive Summary Company or Individual Profile and Background Problem Identification and...

If n is a positive integer, prove that 1 0 (ln x) n dx = (1)

Question:

Step by Step Answer:

n is a positive integer so Thus by repeated application of lHospita...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions