Understanding the Relationship between Functions and Graphs

In summary, the conversation discusses finding the area of a region bounded by two graphs, f(x) = 2x+1 and g(x) = x^2 +1, and determining which is the upper graph over a given interval. The conversation also mentions resources for learning how to distinguish between graphs, and briefly touches on the topic of antiderivatives.
  • #1
sdoman
6
0

Homework Statement



Problem: Find the area of the region that is bounded by the graphs of f(x) = 2x+1, and g(x) = x^2 +1

I have calculated the points of intersection, but am having trouble figuring out which is the upper graph over this interval:

x=0 & x=2

Are there any resources you can point me to so as I can learn to distinguish?

Many thanks in advance.
 
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  • #2
sdoman said:

Homework Statement



Problem: Find the area of the region that is bounded by the graphs of f(x) = 2x+1, and g(x) = x^2 +1

I have calculated the points of intersection, but am having trouble figuring out which is the upper graph over this interval:

x=0 & x=2

Are there any resources you can point me to so as I can learn to distinguish?
  • Brain
  • Hand
  • Paper
  • Pencil
Sketch a graph of the two functions. One graph is a straight line; the other is a parabola.

sdoman said:
Many thanks in advance.
 
  • #3
Ha sounds good man.

Another question:

I have the anti derivative from 0 to 2 (2x-x^2) dx

and then the example states we get (x^2 - (x^3)/3) over the same interval.

My question is about the 2x after we integrate it we get x^2.

So if we have 4x would it be x^2 or x^4?

Thanks
 
  • #4
Do you know any rules for antiderivatives? Do you know how derivatives and antiderivatives are related?
 
  • #5
I am having trouble with them.
 
  • #6
I do know the basics in how they are related I guess you could say
 
  • #7
What rules do you know?

sdoman said:
I do know the basics in how they are related I guess you could say
OK, how are they related?
 

FAQ: Understanding the Relationship between Functions and Graphs

1. What is integration and why is it important in science?

Integration is the process of combining different elements or parts into a whole. In science, integration is important because it helps to connect different pieces of information and ideas, leading to a better understanding of complex systems and phenomena.

2. What are some common problems with integration in scientific research?

Some common problems with integration in scientific research include conflicting data or results, difficulty in combining different methodologies or approaches, and challenges in interpreting and synthesizing large amounts of information.

3. How can we overcome problems with integration in scientific research?

To overcome problems with integration in scientific research, it is important to have clear communication and collaboration between researchers from different disciplines, use standardized methods and protocols, and carefully analyze and interpret data to identify any inconsistencies or gaps in knowledge.

4. What are the implications of not addressing integration issues in science?

If integration issues are not addressed in science, it can lead to incomplete or inaccurate understanding of phenomena, hinder progress in research, and potentially impact decision-making and practical applications of scientific findings.

5. How can scientists ensure effective integration in their work?

To ensure effective integration in their work, scientists should prioritize interdisciplinary collaborations, continuously review and analyze their data, and strive for a comprehensive understanding of the system or phenomenon being studied.

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