Integrate Cos√x: Get Started Now!

In summary, to solve for the integral of cos√x, the conversation suggests using substitution and integration by parts. The speaker is unsure of where to start and mentions that no matter what they substitute for U, they will be left without a du. When asked about the limits of integration, it is revealed that the integral is indefinite. The speaker then suggests substituting U=√x and using du=1/2√x. However, they are unsure of how to proceed as they are left with the integral of cos(u) and no du. It is then clarified that du=2udu, and the speaker asks if they can integrate to get u^2 sinu. Finally, it is suggested to use integration by
  • #1
EV33
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0
Integral of cos√x



We are supposed to use substitution and integration by parts but I really don't know where to even start.



No matter what I substitute for U I will be left without a du.
 
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  • #2
what are your limits of integration?...what does your integral become when you use the substitution u=sqrt(x)? What is du?
 
  • #3
There are no limits it is indefinite. If you let U= √x then du= 1/2√x and that is my problem because I am left with with integral of cos(u) and no du.
 
  • #4
doesn't [itex]du=\frac{1}{2\sqrt{x}}dx[/itex] and doesn't that mean that [itex]dx=2 \sqrt{x} du= 2udu[/itex]?
 
  • #5
Yes it does. So does that mean when I integrate I get u^2 sinu and from there I just need to back substitute?
 
  • #6
Well, that means that

[itex]\int cos(\sqrt{x})dx= \int 2ucos(u)du[/itex]

now you'll need to integrate by-parts...try using f(u)=2u and g'(u)=cos(u)du
 
  • #7
oh ok. Thank you for the help.
 

What is the meaning of "Integrate Cos√x"?

"Integrate Cos√x" refers to the process of finding the indefinite integral of the function cos√x, which involves finding a function whose derivative is cos√x.

Why is it important to learn how to integrate cos√x?

Integrating functions, including cos√x, is a fundamental part of calculus and is essential for solving various problems in physics, engineering, and other fields. It also helps in understanding the behavior and properties of different functions.

What are the steps involved in integrating cos√x?

The steps involved in integrating cos√x include applying the chain rule, using trigonometric identities, and using substitution to simplify the integral. It is also important to understand the properties of the cosine function and the rules of integration.

Are there any tips for integrating cos√x more efficiently?

One tip for integrating cos√x more efficiently is to practice and familiarize yourself with the different techniques and strategies for integration, such as integration by parts and trigonometric substitutions. Additionally, breaking down the integral into smaller, simpler parts can make the process easier.

What are some common mistakes to avoid when integrating cos√x?

Some common mistakes to avoid when integrating cos√x include forgetting to apply the chain rule, using incorrect trigonometric identities, and making calculation errors. It is also important to be careful with signs and to double-check your work for accuracy.

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