Integration applications f(x) and g(x)

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Homework Help Overview

The problem involves finding the area between the curves defined by the functions f(x) = x^3 + 4 and g(x) = x^2 - 4x - 2. The original poster expresses difficulty in approaching this task and seeks assistance.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants suggest starting with a sketch of the graphs to understand the area between the curves. There is mention of visualizing the area as composed of thin rectangles to aid in conceptualizing the integration process.

Discussion Status

Some guidance has been provided regarding the initial steps to take, such as sketching the graphs and considering the area in terms of rectangles. The original poster indicates a newfound understanding, although the discussion does not reach a consensus on a complete method.

Contextual Notes

The original poster expresses stress over the homework assignment and requests a step-by-step procedure, indicating a desire for clarity in future similar problems.

DJ-Smiles
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Homework Statement



find the area between the curves f(x)=x^3+4 and g(x)=x^2-4x-2

ok so i am really stuck here my teacher has just given me this question for homework and i have no idea how to do it. I usually don't struggle with maths and seeing as i am with this, i am stressing out majorly, please give me some help in answering this.

If possible i would like a step by step procedure so i know what to do in future
any help is greatly appreciated.
 
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When you are asked to find the area between two curves, you can start by sketching the graph, which will allow you to better understand the shape of the area of the region needed. Show your work.
 
Once you have the graph drawn, imagine breaking the area between the curves into a lot of very thin rectangles, each of width "dx". For any given x, what is the height of the rectangle (in terms of "x")?
 
Thanks for that both of you guys, I understand how to do it now :). Sorry I didn't thank you earlier, I was having trouble with my internet.
 

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