Evaluating Integrals: Additive Interval Property

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Homework Help Overview

The discussion revolves around evaluating a definite integral using the additive interval property of integrals. Participants are presented with specific integral values and are tasked with finding the integral over a different interval.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express confusion about how to apply the additive interval property of integrals. Some attempt to calculate the integral directly, while others discuss the relationship between the areas under the curve represented by the integrals.

Discussion Status

There are multiple interpretations being explored regarding the application of the additive property. Some participants have provided calculations and results, while others are questioning the correctness of their approaches. Guidance has been offered to consider the areas under the curve, but no consensus has been reached on the final evaluation.

Contextual Notes

Participants are working with specific integral values and are trying to deduce the value of another integral based on those. There is an emphasis on understanding the relationship between different intervals and their corresponding areas.

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Homework Statement




Given
7 f(x) dx= 8
0

7 f(x) dx = −3
1

evaluate the following.

1 f(x) dx
0



Homework Equations


n/a


The Attempt at a Solution



I'm a little confused on how to approach this problem. Do i use the additive interval property of integrals?
 
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mathpat said:

Homework Statement




Given
7 f(x) dx= 8
0

7 f(x) dx = −3
1

evaluate the following.

1 f(x) dx
0



Homework Equations


n/a


The Attempt at a Solution



I'm a little confused on how to approach this problem. Do i use the additive interval property of integrals?
Yes.
 
I ended up with 5. Is that correct?
 
Last edited:
mathpat said:
I ended up with 5. Is that correct?
So 5 + (-3) = 8?
 
To expand on what Mark44 is saying, remember that these integrals represent areas under your curve, f(x). If you know how much area is under the curve between x = 0 and x = 7 and also know how much area is under the curve between x = 1 and x = 7, can you intuitively decide how to find the area between x = 0 and x = 1?
 
Yea I understand but when I use the formula i keep getting 5. I don't see where I'm going wrong.
 
\int_0^7 f(x) dx = \int_0^1 f(x) dx + \int_1^7 f(x) dx. What happens when you plug in what you know?
 
I calculated 11 using that formula.
 
Good, that's right.
 
  • #10
Thanks
 

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