Important intergration substitution

In summary, the conversation discusses how to solve the integral int^{0}_{t}[cos(sqrt{x}]dx. The person providing assistance suggests using a substitution to eliminate the square root and then using a method for integrating products of two functions. They also mention the proper use of LaTeX for formatting.
  • #1
rs8910
1
0
int^{0}_{t}[cos(sqrt{x}]dx can anyone tell me the solution to this question !
 
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  • #2
Welcome to PF rs8910. You should note that homework is to be threaded in the homework help section, and any homework must be accompanied by reasonable evidence that you have given the question a fair shot, which means including working and where you are stuck.

I can give you some limited help though. First let try a substitution that would get rid of that square root sign, and try some method of integrating products of 2 functions.

EDIT: I see you have given [tex]\LaTeX[/tex] a good shot, but you still need to learn how to use it properly. To see what something typed to form the TeX you see, just press on the image. It will also link you to a LaTeX guide.
 

1. What is important integration substitution?

Important integration substitution is a method used in calculus to simplify the process of integration by substituting a variable in the integral with another variable or expression. This allows for easier integration and can often lead to a simpler solution.

2. How do you perform important integration substitution?

To perform important integration substitution, first identify a variable or expression within the integral that can be substituted with another variable. Then, choose a substitution that will make the integral easier to solve. Finally, integrate the new expression with respect to the substituted variable and then substitute back in the original variable at the end.

3. When should I use important integration substitution?

Important integration substitution is most useful when the integral being solved involves a complicated expression or when the integral contains a function that is difficult to integrate. It can also be beneficial when the integral contains a trigonometric function.

4. What are the benefits of using important integration substitution?

Using important integration substitution can make integration easier and lead to a simpler solution. It can also help to solve integrals that may have been difficult or impossible to solve without substitution. Additionally, it can be used to solve integrals involving trigonometric functions.

5. Are there any limitations to using important integration substitution?

While important integration substitution can be a useful tool in integration, it may not always be applicable or result in a simpler solution. In some cases, the substitution may lead to a more complicated integral or may not be possible to perform. It is important to carefully choose the substitution and evaluate its effectiveness in each individual case.

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