Homework Help is Here – Start Your Trial Now!
Math
Calculus
[ (2x² - 6x +) dx and interpret the result EXAMPLE 4 Find in terms of areas. SOLUTION The Fundamental Theorem gives [ (2x* - 6x + ) ak = 2() - ) • tan" 3 x2 + 1 dx = + 3 tan- - 3x2 + 3 tan-1 =글(2)-3(27) + 3 tan-I(2) - | + 3 tan-(2). This is the exact value of the integral. If a decimal approximation is desired, we can use a calculator to approximate tan-(2). Doing so, we get 3 - 6x + |dx = . (Round your answer x2 + 1 to four decimal places.) The figure below shows the graph of the integrand. We know that the value of the integral can be interpreted as a net area: the sum of the areas labeled with a plus sign minus the area labeled with a minus sign. +,

[ (2x² - 6x +) dx and interpret the result EXAMPLE 4 Find in terms of areas. SOLUTION The Fundamental Theorem gives [ (2x* - 6x + ) ak = 2() - ) • tan" 3 x2 + 1 dx = + 3 tan- - 3x2 + 3 tan-1 =글(2)-3(27) + 3 tan-I(2) - | + 3 tan-(2). This is the exact value of the integral. If a decimal approximation is desired, we can use a calculator to approximate tan-(2). Doing so, we get 3 - 6x + |dx = . (Round your answer x2 + 1 to four decimal places.) The figure below shows the graph of the integrand. We know that the value of the integral can be interpreted as a net area: the sum of the areas labeled with a plus sign minus the area labeled with a minus sign. +,

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
EXAMPLE 4 Find 6х + dx and interpret the result x² + 1 in terms of areas. SOLUTION The Fundamental Theorem gives 2() - G) - 6x + dx = + 3 tan-1 x2 + 1 3x2 + 3 tan 극(24)-3(22) + 3 tan-1(2) - + 3 tan-1(2). This is the exact value of the integral. If a decimal approximation is desired, we can use a calculator to approximate tan-(2). Doing so, we get - 6x +) ax = ( 3 (Round your answer x² + 1 to four decimal places.) The figure below shows the graph of the integrand. We know that the value of the integral can be interpreted as a net area: the sum of the areas labeled with a plus sign minus the area labeled with a minus sign. y 3 X 2
Transcribed Image Text:EXAMPLE 4 Find 6х + dx and interpret the result x² + 1 in terms of areas. SOLUTION The Fundamental Theorem gives 2() - G) - 6x + dx = + 3 tan-1 x2 + 1 3x2 + 3 tan 극(24)-3(22) + 3 tan-1(2) - + 3 tan-1(2). This is the exact value of the integral. If a decimal approximation is desired, we can use a calculator to approximate tan-(2). Doing so, we get - 6x +) ax = ( 3 (Round your answer x² + 1 to four decimal places.) The figure below shows the graph of the integrand. We know that the value of the integral can be interpreted as a net area: the sum of the areas labeled with a plus sign minus the area labeled with a minus sign. y 3 X 2
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS