# Trigonometric Substitution Problem - Calculus 2

• khatche4
In summary, the conversation discusses a trig substitution for a Calculus 2 class and the confusion about starting the problem. The professor has not covered how to evaluate trigonometric substitutions with coefficients, and there is a question about factoring out the two in the equation. The solution is to factor out the two as \sqrt{3-2x^2} is equivalent to \sqrt{2}*\sqrt{\frac{3}{2}-x^2}.
khatche4
Hey there
This is a trig substitution for my Calculus 2 class and I really have NO idea how to get started...

$$\int\frac{4}{\sqrt{3-2x^2}}dx$$

My professor has yet to go over how to evaluate trigonometric substitutions with coefficients in front of variables.

how about factoring out the 2?

How would you factor out the two?

Because $$\sqrt{3-2x^2}$$ is not the same as 2*$$\sqrt{\frac{3}{2}-x^2}$$

khatche4 said:
How would you factor out the two?

Because $$\sqrt{3-2x^2}$$ is not the same as 2*$$\sqrt{\frac{3}{2}-x^2}$$

Yes, but $$\sqrt{3-2x^2} = \sqrt{2}*\sqrt{\frac{3}{2}-x^2}$$. I may not have been clear in my previous post.

Oh! Duh! Thank you!
I'll give it a try.

## 1. What is trigonometric substitution?

Trigonometric substitution is a technique used in calculus 2 to solve integrals that involve radicals or quadratic expressions. It involves substituting trigonometric functions for variables in the integral to simplify the problem.

## 2. When should I use trigonometric substitution?

Trigonometric substitution is typically used when dealing with integrals that involve square roots, or when the integrand can be rewritten as a quadratic expression. It can also be used to simplify complicated algebraic expressions.

## 3. How do I know which trigonometric function to substitute?

The choice of trigonometric function to substitute depends on the form of the integral. For integrals involving the square root of a quadratic expression, the appropriate substitution is typically made by setting the variable equal to the tangent, secant, or cosecant of an angle. For other forms, such as integrals involving the sum or difference of squares, other substitutions may be needed.

## 4. What are some common mistakes to avoid when using trigonometric substitution?

Some common mistakes include forgetting to change the limits of integration, not properly substituting for all variables, and not simplifying the final answer. It is also important to be familiar with trigonometric identities and their derivatives to avoid errors in the substitution process.

## 5. Are there any alternative techniques to solve integrals besides trigonometric substitution?

Yes, there are several other techniques, such as integration by parts, partial fractions, and u-substitution. The choice of technique depends on the form of the integral and the individual's preference. It is always helpful to try different techniques and see which one leads to the simplest solution.

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