- #1
Can someone please check my answer: Trig Substitution problem
- Thread starter jimen113
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In summary, a trig substitution problem is a mathematical problem that involves using trigonometric identities and functions to solve an integral. It is typically used when solving integrals with expressions involving radicals or trigonometric functions. The steps for solving a trig substitution problem include identifying the appropriate substitution, simplifying the integral using trigonometric identities, and then solving the integral using standard techniques. Common mistakes to avoid include forgetting to substitute for the variable and not simplifying the integral before solving. To master trig substitution problems, practice and familiarity with trigonometric identities and functions are important, as well as double-checking answers and being aware of common mistakes to avoid.
- #2
HallsofIvy
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If you are letting [itex]x= cos(\theta)[/itex] then [itex]dx= cos(\theta)d\theta[/itex]. It looks to me like you forgot that [itex]cos(\theta)[/itex].
- #3
- #4
Mark44
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If x = cos([itex]\theta[/itex]), then dx = -sin([itex]\theta[/itex])d[itex]\theta[/itex]
- #5
HallsofIvy
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Yes, of course Mark44 is right. I don't know what came over me!
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jimen113
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Thanks Mark44! that negative sign is sure important...
Related to Can someone please check my answer: Trig Substitution problem
1. What is a trig substitution problem?
A trig substitution problem is a type of mathematical problem that involves using trigonometric identities and functions to solve an integral.
2. How do I know when to use trig substitution?
Trig substitution is typically used when solving integrals that involve expressions with radicals, especially when there is a combination of x^2 and a^2 + x^2 or x^2 - a^2. It can also be used to simplify integrals with trigonometric functions.
3. Can you explain the steps for solving a trig substitution problem?
The first step is to identify which trigonometric substitution to use based on the form of the integral. Then, substitute the appropriate trigonometric function for the variable in the integral. Next, use trigonometric identities to simplify the integral. Finally, solve the integral using standard integration techniques.
4. What are some common mistakes to avoid when solving a trig substitution problem?
One common mistake is forgetting to substitute for the variable in the integral with the appropriate trigonometric function. It is also important to remember to simplify the integral using trigonometric identities before attempting to solve it. Additionally, be careful when evaluating trigonometric functions at specific values, as it can lead to incorrect answers.
5. Are there any tips for mastering trig substitution problems?
Practice is key for mastering trig substitution problems. Make sure to familiarize yourself with common trigonometric identities and functions. It can also be helpful to work through examples and practice problems to gain a better understanding of the process. Additionally, double-check your answers and be aware of common mistakes to avoid.
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