Definite Integral with u/du subsitition

In summary, the conversation is about evaluating an indefinite integral using the u and du substitution method. The person asking for help gets stuck at the last step and is unsure of what to do with the 2 in front of u^(1/2). They are advised to leave it and integrate both terms.
  • #1
Knight226
16
0

Homework Statement


Evaluate the indefinite integral by the method shown in Example 5. (the example in the book is just using the u and du substitution)

MathHelp1-1.jpg


Homework Equations


None.

The Attempt at a Solution



The question is right below the instruction and after that question is my steps. Please correct me if I have made mistake somewhere along the way or if I am doing it incorrectly. I get stuck at the last step because I am not sure what I should do to the 2 in front of u^1/2. Please help. Thank you very much.

I don't know how to use the math codes in the forum... so I am attaching a screen shot instead. Thank you.

MathHelp1.jpg
 
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  • #2
The substitution went just fine. I'm not sure what you want to do with the '2'. Just leave it there and try to integrate both terms du. Can you do that?
 
  • #3
Thank you.
I apologize for my careless. I got confused with the book example >.<.
 

FAQ: Definite Integral with u/du subsitition

What is the concept behind u/du substitution in definite integrals?

The concept behind u/du substitution is to simplify the integral by substituting the variable u for a complicated expression within the integral. This substitution allows us to transform the integral into a simpler form that can be easily evaluated using commonly known integration rules.

How do you know when to use u/du substitution in a definite integral?

You should use u/du substitution when the integral involves an expression that can be simplified by substituting it with a new variable u. This is often the case when the integral contains a polynomial, trigonometric, or exponential function.

Can you provide an example of how to use u/du substitution in a definite integral?

Sure, let's take the integral of x^2 * (3x+1)^4, where we can use u/du substitution by letting u = 3x+1. This transforms the integral into ∫ u^4 * (u-1) du, which can be easily evaluated using integration rules.

What are the benefits of using u/du substitution in a definite integral?

The main benefit of using u/du substitution is that it simplifies the integral and makes it easier to evaluate. It also allows us to solve more complex integrals by breaking them down into simpler forms.

Are there any limitations or restrictions when using u/du substitution in a definite integral?

Yes, there are some limitations and restrictions when using u/du substitution. These include making sure that the new variable u is a function of the original variable x, and that the limits of integration are also expressed in terms of u. Additionally, u/du substitution may not always work for all integrals, and other integration techniques may need to be used.

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