Why cant i use substitution for this?

And it works perfectly. So, why do you think substitution doesn't work?In summary, substitution can be used to find 0∫2 sqrt(4-x^2) by making the substitution x=2cos(θ). This substitution works effectively and it is unclear why it was thought that substitution would not work for this integral.
  • #1
schapman22
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Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.
 
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  • #2
schapman22 said:
Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.

If you make the substitution [itex] u=x^2 [/itex] then du = 2x dx. But you don't have a factor of 2x in the integrand. Or were you thinking of a different substitution? In any case, a trigonometric substitution would work better.
 
  • #3
schapman22 said:
Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.

But substitution does work. Make the substitution x = 2cos(θ). Isn't that a "substitution"?
 

1. Why can't I use substitution for this mathematical problem?

Substitution is a valid method for solving equations, but it may not always be the most efficient or accurate method. Depending on the complexity of the problem and the variables involved, other methods such as elimination or graphing may be more appropriate.

2. Can substitution be used for all types of equations?

No, substitution can only be used for linear equations, where the variables have a power of 1. It cannot be used for equations with variables raised to a higher power, such as quadratic or cubic equations.

3. How do I know when to use substitution?

You can use substitution when you have two or more equations with the same number of variables and the coefficients of the variables are the same. This allows you to solve for one variable in one equation and substitute it into the other equations to find the values of the remaining variables.

4. Are there any drawbacks to using substitution?

One drawback of using substitution is that it can be time-consuming, especially for equations with multiple variables. It also may not always provide an exact or accurate solution, as rounding errors can occur when substituting values into the equations.

5. Can substitution be used in real-world problems?

Yes, substitution can be used in real-world problems, especially when dealing with systems of linear equations. It can be used to find the intersection point of two lines, which can represent real-world situations such as finding the break-even point in a business or the optimal solution to a manufacturing problem.

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