Integral problem, does b & a change sometime in the problem?

In summary, the conversation is about problem number 16, which involves changing the limits of integration by making a substitution. The person is asking for clarification on when and why the limits change, to which the expert explains that it depends on the substitution being made.
  • #1
pillar
35
0
Problem number 16
http://img29.imageshack.us/img29/3179/38653938.png
For the record the y at the end is cubed. Thanks in advance.
 
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  • #2
If you are referring to the limits of integration, then yes they change if you make the proper substitution that makes this integral very easy.
 
  • #3
What do you mean by: "do b and a change sometime?" Are you talking about the limits of integration changing?
 
  • #4
Feldoh said:
What do you mean by: "do b and a change sometime?" Are you talking about the limits of integration changing?

Yes the bounds or limits. b=2 and a=0 Why do they change to other numbers later on during the problem?
 
  • #5
If you substitute, for example, [tex]u=1+y^3[/tex], then the limits will change from ya=0, yb=2 to ua=1 and ub=9. That's because you're integrating with respect to u instead of y.
 

1. How does changing b and a affect the integral problem?

Changing b and a can alter the limits of integration, which in turn can change the value of the integral. It can also affect the shape of the integrand function, leading to a different result.

2. Can the integral problem still be solved if b and a are changed?

Yes, the integral problem can still be solved as long as the new limits of integration are within the domain of the integrand function.

3. Is it necessary to know the specific values of b and a to solve the integral problem?

No, it is not necessary to know the specific values of b and a. The integral problem can be solved using symbolic notation, which allows for a more general solution that can be applied to various values of b and a.

4. How can changing b and a affect the accuracy of the integral solution?

If the limits of integration are changed to values that are too close together, it can lead to a less accurate solution due to the limited precision of numerical integration methods. However, if the new limits are appropriately chosen, the accuracy should not be affected.

5. In which types of problems would changing b and a be necessary?

Changing b and a may be necessary in problems where the integrand function changes or is undefined at certain values, or when the area to be calculated is not within the original limits of integration. It can also be used to test the sensitivity of the integral solution to different limits of integration.

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