Explanation Formula used: ∫ u 2 − a 2 d u = 1 2 ( u u 2 − a 2 − a 2 ln | u + u 2 − a 2 | ) Calculation: The given integral is ∫ x x 4 − 16 d x . Let u 2 = x 4 . Then, u = x . Differentiate u = x to obtain the value of d x . Thus, d x = 1 2 u d u . Substitute u = x , u 2 = x 4 and d x = 1 2 u d u in the given integral. Then the integral can be rewritten as follows. ∫ x x 4 − 16 d x = ∫ u u 2 − 16 ( d u 2 u ) = 1 2 ∫ u 2 − 16 d u The integral ∫ u 2 − 16 d u is similar to ∫ u 2 − a 2 d u , where a = 4 . By using the above formula the given integral can be evaluated as follows

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 6.4, Problem 42E

To determine

To evaluate: The given indefinite integral ∫xx4−16dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 41E

Chapter 6.4, Problem 43E

Students have asked these similar questions

No chatgpt pls will upvote

Title: Analyzing Customer Satisfaction for UnileverAs a member of Unilever's Customer Experience Management team, you are responsible forevaluating customer satisfaction levels and monitoring competitive moves. This case studyinvolves analyzing satisfaction data to test two key hypotheses about Unilever's performancerelative to its main competitor, Procter & Gamble (P&G).Unilever’s leadership team has emphasized the importance of customer satisfaction inmaintaining competitive advantage and market leadership. As part of this initiative, yourteam regularly monitors satisfaction scores and benchmarks them against competitors likeP&G.You are tasked with analyzing the provided dataset to answer the following questions:1. Does Unilever’s average customer satisfaction score meet the minimum threshold of2. 75%?Is there no significant difference between Unilever’s overall average satisfaction scoreand P&G’s average satisfaction score?

Please help me first one graphically and the other in matrix

Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 8MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The given indefinite integral ∫ x x 4 − 16 d x .

Solution Summary: The author evaluates the value of the given indefinite integral sqrtx416dx.

Concept explainers

Videos

To evaluate: The given indefinite integral ∫xx4−16dx.

Want to see the full answer?

Chapter 6 Solutions