Explanation Given: The curves are y = x 5 − 2 ln ( x + 5 ) , and y = x 3 − 2 ln ( x + 5 ) . Approach: If f and g are continuous function and f ( x ) ≥ g ( x ) on [ a , b ] , then the area between the curves f ( x ) and g ( x ) from x = a to x = b is given as, A = ∫ a b [ f ( x ) − g ( x ) ] d x ... ( 1 ) Here, A is the area between the curves. Calculation: To find point of intersection solve the curves as, x 5 − 2 ln ( x + 5 ) = x 3 − 2 ln ( x + 5 ) x 5 − x 3 = 0 x 3 ( x − 1 ) ( x + 1 ) = 0 x = − 1 , 0 , 1 Substitute − 1 for x in y = x 3 − 2 ln ( x + 5 ) . y = ( − 1 ) 3 − 2 ln ( ( − 1 ) + 5 ) = − 1 − 2 ln 4 = − 3.773 Substitute 0 for x in y = x 3 − 2 ln ( x + 5 ) . y = ( 0 ) 3 − 2 ln ( ( 0 ) + 5 ) = − 2 ln 5 = − 3.219 Substitute 1 for x in y = x 3 − 2 ln ( x + 5 ) . y = ( 1 ) 3 − 2 ln ( ( 1 ) + 5 ) = 1 − 2 ln 6 = − 2.584 The points of intersection are ( − 1 , − 3.773 ) , ( 0 , − 3.219 ) , and ( 1 , − 2.584 ) . The graphical representation of the region enclosed by the curves is shown below as, Figure ( 1 ) Substitute x 5 − 2 ln ( x + 5 ) for f ( x ) and x 3 − 2 ln ( x + 5 ) for g ( x ) from x = − 1 to x = 0 and also substitute x 3 − 2 ln ( x + 5 ) for f ( x ) and x 5 − 2 ln ( x + 5 ) for g ( x ) from x = 0 to x = 1 in equation ( 1 )

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

See similar textbooks

Videos

Question

Chapter 7.5, Problem 20E

To determine

To find:

The area between the curves y=x5−2ln(x+5), and y=x3−2ln(x+5).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.5, Problem 19E

Chapter 7.5, Problem 21E

Students have asked these similar questions

Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations).

Vectors u and v are shown on the graph.Part A: Write u and v in component form. Show your work. Part B: Find u + v. Show your work.Part C: Find 5u − 2v. Show your work.

Vectors u = 6(cos 60°i + sin60°j), v = 4(cos 315°i + sin315°j), and w = −12(cos 330°i + sin330°j) are given. Use exact values when evaluating sine and cosine.Part A: Convert the vectors to component form and find −7(u • v). Show every step of your work.Part B: Convert the vectors to component form and use the dot product to determine if u and w are parallel, orthogonal, or neither. Justify your answer.

Chapter 7 Solutions

EBK CALCULUS FOR THE LIFE SCIENCES

Ch. 7.1 - YOUR TURN Find an antiderivative of f(x)=8x7.Ch. 7.1 - Prob. 2YT Ch. 7.1 - Prob. 3YT Ch. 7.1 - Prob. 4YT Ch. 7.1 - Prob. 5YT Ch. 7.1 - Prob. 6YT Ch. 7.1 - YOUR TURN Find an equation of the curve whose...Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E

Knowledge Booster

$Calculus$

Learn more about

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

The area between the curves y = x 5 − 2 ln ( x + 5 ) , and y = x 3 − 2 ln ( x + 5 ) .

Solution Summary: The author explains that the area between the curves is 16.

Videos

To find:

The area between the curves y=x5−2ln(x+5), and y=x3−2ln(x+5).

Want to see the full answer?

Chapter 7 Solutions

The area between the curves y = x 5 − 2 ln ( x + 5 ) , and y = x 3 − 2 ln ( x + 5 ) .

Solution Summary: The author explains that the area between the curves is 16.

Videos

To find: The area between the curves y=x5−2ln(x+5), and y=x3−2ln(x+5).

Want to see the full answer?

Chapter 7 Solutions

To find:

The area between the curves y=x5−2ln(x+5), and y=x3−2ln(x+5).