# Integration by Parts: Improper Integral

• ggcheck
In summary, using u substitution, the expression given can be simplified to (u+3)/u^1/2 = u^1-1/2 +3u^-1/2. This eliminates the need for integration by parts and solves the problem.
ggcheck
I used u substitution to get to this point:

$$\lim_{R\rightarrow\ 3-}} \int_{-3}^{R-3} (\frac{u + 3}{sqrt{u}}) du$$

is the only way to proceed from here using integration by parts?

Last edited:
ggcheck said:
I used u substitution to get to this point:

$$\lim_{R\rightarrow\ 3-}} \int_{-3}^{R-3} (\frac{u + 3}{sqrt{u}}) du$$

is the only way to proceed from here using integration by parts?

If your calculations are correct up to this point, i do not think you need to use integ by parts. Simply just try to rearrange the integrand like this

(u+3)/u^1/2= u/u^1/2 +3/u^1/2 = u^1-1/2 +3u^-1/2 and i guess you will be fine!

sutupidmath said:
If your calculations are correct up to this point, i do not think you need to use integ by parts. Simply just try to rearrange the integrand like this

(u+3)/u^1/2= u/u^1/2 +3/u^1/2 = u^1-1/2 +3u^-1/2 and i guess you will be fine!
ahhh, I didn't think to break up the fraction, for some reason I missed that

thanks :)

## 1. How can integration by parts be used to evaluate improper integrals?

Integration by parts is a technique used to evaluate integrals that involve a product of two functions. By breaking down the integral into smaller parts and applying the integration by parts formula, it is possible to simplify the integral and find a solution. This method is particularly useful for improper integrals, which do not have finite limits of integration.

## 2. What is the integration by parts formula?

The integration by parts formula is:

∫ u(x)v(x) dx = u(x) ∫ v(x) dx - ∫ u'(x) ∫ v(x) dx

where u(x) and v(x) are two functions, and u'(x) is the derivative of u(x).

## 3. How do I determine which function to choose as u(x) and which to choose as v(x)?

When choosing u(x) and v(x), it is important to consider which function will simplify after taking the derivative and which function will become simpler after being integrated. Generally, the function that becomes simpler after being differentiated should be chosen as u(x) and the function that becomes simpler after being integrated should be chosen as v(x).

## 4. Can integration by parts be used for all types of integrals?

No, integration by parts is most effective for integrals that involve a product of two functions. It may not work for other types of integrals, such as trigonometric or exponential functions, where other integration techniques may be more suitable.

## 5. Are there any limitations to using integration by parts?

Yes, integration by parts may not always result in a solution. It is important to check if the integral can be solved using other techniques as well. Additionally, integration by parts may not work for integrals with infinitely oscillating functions or those that do not converge.

Replies
7
Views
1K
Replies
22
Views
2K
Replies
16
Views
2K
Replies
5
Views
858
Replies
15
Views
1K
Replies
1
Views
1K
Replies
3
Views
873
Replies
21
Views
1K
Replies
6
Views
1K
Replies
27
Views
2K