# Use substitution to evaluate the integral

• Inept
In summary, substitution is used to evaluate integrals when there is a function within a function or a pattern in the integrand. The process involves identifying the function to substitute, finding its derivative, and using basic integration techniques. Substitution is not always applicable, and it is important to choose the appropriate method for evaluation. There is no specific order for substitutions, but it is important to choose one that simplifies the integral. Common mistakes include forgetting to substitute the differential and choosing the wrong function to substitute. Checking the answer by differentiating is recommended.
Inept

## Homework Statement

Use substitution to evaluate the integral

## Homework Equations

∫√(cotx) csc^(2)x dx?

i tried, but i really have no idea what to do with the sqrt

What's the derivative of cot(x)? What do you think your substitution should be based on that?

i feel stupid.
thanks

## 1. How do I know when to use substitution to evaluate an integral?

Substitution is typically used when the integrand contains a function within a function, or when there is a chain rule involved. This can also be identified by looking for a pattern in the integrand, such as a polynomial raised to a power or a trigonometric function multiplied by its derivative.

## 2. What is the process for using substitution to evaluate an integral?

The first step is to identify the function that needs to be substituted, usually denoted by u. Then, find the derivative of u and use that to replace the function within the integral. After substituting, the integral can be evaluated using basic integration techniques.

## 3. Can substitution be used for all integrals?

No, substitution is not always necessary or applicable for evaluating integrals. Some integrals can be solved using other techniques, such as integration by parts or partial fractions. It is important to identify the integral and choose the appropriate method for evaluation.

## 4. Is there a specific order in which substitutions should be made?

In general, there is no specific order for substitutions. However, it is important to choose a substitution that will simplify the integral and make it easier to evaluate. Sometimes, multiple substitutions may be necessary to fully simplify the integral.

## 5. Are there any common mistakes to watch out for when using substitution to evaluate an integral?

One common mistake is forgetting to substitute the differential, dx, when making the substitution. It is also important to be careful when choosing the function to substitute, as it can greatly affect the difficulty of the integral. It is always helpful to check the answer by differentiating it to ensure it is correct.

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