Finding the area between curves

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The discussion focuses on finding the area between the curves defined by the equations y = x^5 - 2ln(x+5) and y = x^3 - 2ln(x+5). Participants identify the intersection points, noting that they occur at x = 0 and x = 1, which serve as the limits for the integral needed to calculate the area. There is some confusion regarding the mention of x = 9.24, which is clarified as incorrect, and the importance of sketching the graph to visualize the intersections is emphasized. The conversation highlights the necessity of solving the equation where the two curves equal each other to determine the exact points of intersection. Understanding these intersections is crucial for accurately calculating the area between the curves.
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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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