Finding an integral given two other integrals?

In summary, the integral from 4 to 16 is 6. This can be found by using the properties of integrals and subtracting the integral from 1 to 4 from the integral from 1 to 16.
  • #1
JessicaJ283782
41
0

Homework Statement



It is given that

integral(1 to 2) g(x)dx=22
integral (1 to 4) g(x)dx=7
integral (1 to 16) g(x)dx=13

Find integral (4 to 16)


Homework Equations



Using properties of integrals, integral(4 to 16)= integral(1 to 16) - integral(1 to 4)


The Attempt at a Solution



So, you can ignore the in integral (1 to 2) since it is not in the interval you need to solve for.

Integral(1 to 16) - integral(1 to 4) = 13-7 =6

The integral from (4 to 16) = 6

Am I correct?
 
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  • #2
JessicaJ283782 said:

Homework Statement



It is given that

integral(1 to 2) g(x)dx=22
integral (1 to 4) g(x)dx=7
integral (1 to 16) g(x)dx=13

Find integral (4 to 16)


Homework Equations



Using properties of integrals, integral(4 to 16)= integral(1 to 16) - integral(1 to 4)


The Attempt at a Solution



So, you can ignore the in integral (1 to 2) since it is not in the interval you need to solve for.

Integral(1 to 16) - integral(1 to 4) = 13-7 =6

The integral from (4 to 16) = 6

Am I correct?

Yes, you are.
 

1. What is the purpose of finding an integral given two other integrals?

The purpose of finding an integral given two other integrals is to simplify the process of solving complex integrals by breaking them down into smaller, more manageable parts. It allows us to use known integrals to find the value of a new integral without having to evaluate it directly.

2. How do you find an integral given two other integrals?

There are several methods for finding an integral given two other integrals, such as using integration by parts, substitution, or trigonometric identities. The specific method used will depend on the given integrals and their relationship to each other.

3. Can any two integrals be used to find a third integral?

No, not all pairs of integrals can be used to find a third integral. The two given integrals must have a specific relationship to each other, such as being the derivatives of the same function, in order for the third integral to be found.

4. Are there any limitations to finding an integral given two other integrals?

Yes, there are limitations to finding an integral given two other integrals. For example, the two given integrals must be continuous and defined on the same interval for the third integral to be found. Additionally, the relationship between the two integrals must be known and solvable using a known integration technique.

5. How can finding an integral given two other integrals be useful in real-world applications?

Finding an integral given two other integrals can be useful in real-world applications where complex integrals arise, such as in physics, engineering, or economics. It allows for the simplification of calculations and can make solving complicated problems more efficient.

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