Finding the area between curves

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Homework Help Overview

The discussion revolves around finding the area between two curves defined by the equations y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5). Participants are exploring how to determine the limits of integration by identifying the intersection points of the curves.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to find intersection points to establish limits for integration. There is uncertainty about the correct intersection points, with some suggesting x = 9.24, while others propose x = 0 and x = 1 as valid limits. Questions arise regarding the method to determine these points and the values of the curves at these intersections.

Discussion Status

The discussion is active, with participants questioning the validity of proposed intersection points and seeking clarification on how to approach the problem. Some guidance has been offered regarding the nature of intersections, but there is no consensus on the correct limits or the method to solve for them.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the tools or methods they can use to solve the problem. There is also a mention of potential confusion regarding the intersection points, indicating a need for careful consideration of the equations involved.

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Homework Statement



y = x^5 - 2ln(x+5)

and

y = x^3 - 2ln(x+5)


Homework Equations





The Attempt at a Solution



i put it ont he calculator but i honestly don't even no where the spot that i amtrying to find the area for is
 
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well find where they intersect and you will find the limits of the required integral
 
they intersect at x = 9.24?
 
They also pretty clearly intersect at 0.
 
ok so now how do i get started with that
 
Actually, I wasn't paying attention. How did you get 9.24 as an intersection point? They intersect at x = 0 and x = 1. Those are the limits of integration that are desired I imagine.
 
yea i don't even no where the 9.24 came from.. so i do it from x=0 to x=1 and what is the top and bottom values??
 
Uh, I didn't sketch the graph when I did this, but isn't x=-1 also a possible intersection point?
 
One of the very first things you should have learned is that two curves intersect where the same x-value gives the same y-value.

The graphs of y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5) intersect where
y= x^5- 2ln(x+5)= x^3- 2ln(x+5). Can you solve that equation?
 

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