2.6.62 inverse integrals with substitution

In summary, the conversation is about a document on Overleaf that contains many custom macros which cannot be pasted into the code easily. The person is unsure about all the details but appreciates any comments. The topic of discussion is about the usage of b, x, and u in the document and there may be some errors in substitution. The conversation also mentions a mistake in the solution for problem 6.6.62 that should be corrected.
  • #1
karush
Gold Member
MHB
3,269
5
View attachment 9266
ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
 

Attachments

  • 253a.PNG
    253a.PNG
    5.1 KB · Views: 101
Last edited:
Physics news on Phys.org
  • #2
karush said:
ok this is from my overleaf doc
so too many custorm macros to just paste in code
but I think its ok,,, not sure about all details.
appreciate comments...

I got ? somewhat on b and x and u being used in the right places
Ummm...

What exactly is your question?

-Dan
 
  • #3
OK this one was kinda obvious but usually that is where I make the errors especially where there is substitution.
I post another one here soon.:cool:
 
  • #4
karush said:
View attachment 9267
That all looks correct to me, except that at one point in the solution of 6.6.62 you have written $du=dx$. That should be $\dfrac{du}4 = dx$ (which is what you have correctly used in the following line).
 

Attachments

  • 253a.PNG
    253a.PNG
    5.1 KB · Views: 71

1. What is the concept of inverse integrals with substitution?

The concept of inverse integrals with substitution is a technique used in calculus to evaluate integrals that cannot be solved using basic integration methods. It involves substituting a variable with a new expression in order to simplify the integral and make it solvable.

2. How do you know when to use inverse integrals with substitution?

Inverse integrals with substitution are typically used when the integrand (the function being integrated) contains a complicated expression or a variable raised to a power. This technique can also be used when the integrand involves trigonometric functions or logarithmic functions.

3. What is the process for solving a 2.6.62 inverse integral with substitution?

The process for solving a 2.6.62 inverse integral with substitution involves first identifying the variable to be substituted, then selecting a suitable substitution expression. The next step is to rewrite the integral in terms of the new variable, and then solve the integral using basic integration techniques. Finally, the solution is converted back to the original variable.

4. What are some common mistakes to avoid when using inverse integrals with substitution?

One common mistake when using inverse integrals with substitution is incorrectly identifying the variable to be substituted. Another mistake is choosing an unsuitable substitution expression, which can result in a more complicated integral. It is also important to carefully convert the solution back to the original variable to avoid errors.

5. Can inverse integrals with substitution be used for definite integrals?

Yes, inverse integrals with substitution can be used for definite integrals. In this case, the limits of integration must also be converted to match the new variable. The solution will then be in terms of the new variable, so it must be converted back to the original variable before evaluating the definite integral.

Similar threads

B Integration by parts of inverse sine, a solved exercise, some doubts...
    • Calculus
Replies
4
Views
917
MHB 1.8.4 AP Calculus Exam Integral of piece-wise function
    • Calculus
Replies
4
Views
2K
I Substitution in a definite integral
    • Calculus
Replies
6
Views
1K
I Integrating a product of exponential and trigonometric functions
    • Calculus
Replies
21
Views
825
I What's my mistake in this integration problem?
    • Calculus
Replies
8
Views
431
B Some questions regarding the integral of cos(ax), "a" not zero
    • Calculus
Replies
16
Views
1K
B Trigonometric substitution, a case I'd like to share
    • Calculus
Replies
3
Views
1K
I Did Math DF's integral calculator make a glaring mistake?
    • Calculus
Replies
8
Views
184
B Justification for cancelling dx in an integral
    • Calculus
Replies
4
Views
3K
I Integral representation of incomplete gamma function
    • Calculus
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top