Area Under Curves (Integrals)

  • Thread starter LadiesMan
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  • #1
LadiesMan
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Suppose the area of the region between the graph of a positive continuous function f and the x-axis from x = a to x = b is 4 square units. Find the area between the area between the curves y = f(x) and y = 2f(x) from x = a to x = b.

Attempt:

Since 2 f(x) is greater than f(x) we can call it g(x) and that will be the dominant function.

[tex]\int (g(x) - f(x)) dx[/tex]

It becomes...
[tex]G(x) - F(x)[/tex]

What do I do next?

Thanks
 

Answers and Replies

  • #2
Pere Callahan
586
1
You said g(x)=2f(x), so what can you say about the relation between G(x) and F(x) ..?

Note that you want to consider definite integrals

[tex]
\int_a^b{dx(g(x)-f(x))}
[/tex]

Can you simplify g(x)-f(x)..?
 
  • #3
LadiesMan
96
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umm yeah i guess that took me off course.
 
  • #4
LadiesMan
96
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so then how would i do it?
 
  • #5
Pere Callahan
586
1
Uhm,

g(x)-f(x) = 2f(x)-f(x) =...?
 
  • #6
LadiesMan
96
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Umm that equals f(x)
 
  • #7
Pere Callahan
586
1
very good, so
[tex]\int_a^b{dx(g(x)-f(x))}=\int_a^b{dx(2f(x)-f(x))}=\int_a^b{dx(f(x))}=...=?[/tex]
 

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