Integration applications f(x) and g(x)

In summary, to find the area between two curves, first sketch the graph to understand the shape of the region. Then, break the area into thin rectangles with a width of "dx" and determine the height of each rectangle in terms of "x". This will allow you to calculate the total area between the curves.
  • #1
DJ-Smiles
47
0

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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  • #2
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.
 
  • #3
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")?
 
  • #4
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.
 

FAQ: Integration applications f(x) and g(x)

What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is essentially the reverse of taking the derivative of a function.

Why do we integrate functions f(x) and g(x)?

Integrating functions f(x) and g(x) can help us solve various problems in physics, engineering, and other fields. It is a useful tool for finding the total amount of something, such as distance, velocity, or volume.

What are the different methods of integration?

There are several methods for integrating functions, including the power rule, substitution, and integration by parts. Each method has its own set of rules and techniques for solving different types of integrals.

How do I know which method of integration to use?

The method you use for integrating a function depends on the form of the function itself. It is important to identify the type of integral you are working with and then choose the appropriate method to solve it. Practice and experience can also help in determining the best method for a given integral.

Can I use integration to solve real-world problems?

Yes, integration is a powerful tool for solving real-world problems. It can be used to calculate areas, volumes, and other quantities that are important in fields such as physics, engineering, and economics. It is also used in data analysis and statistics to estimate values and quantities.

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