Integral Help: Completing the square?

In summary, the conversation discusses how to approach solving the integral \int^{3}_{0}\frac{x^{2}}{(25-4x^{2})^{\frac{3}{2}}} dx, with the suggestion to use a trig substitution. The poster also reminds the OP to include the "dx" term and suggests using the substitution x=asin\theta.
  • #1
nickclarson
32
0

Homework Statement



[tex]\int^{3}_{0}\frac{x^{2}}{(25-4x^{2})^{\frac{3}{2}}} dx[/tex]

Homework Equations


The Attempt at a Solution



Not sure on where to start. We learned in class how to complete the square, but I'm not sure if that's what I am supposed to use on this problem. Can anybody give me a hint on where to start? it would be greatly appreciated.

Thanks,
Nick

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
Here I would use a trig substitution. Also, you forgot the "dx" term. It is very important.

We have;

[tex]\int^3_0 \frac{x^2}{ ( 5^2 - (2x)^2)^{3/2}} dx[/tex]

Can you think of a trig substitution that would make that denominator simpler?
 
  • #3
Oh yea whoops, hmm. [tex]x= asin\theta[/tex]? I'll give it a shot and see what happens. Thanks!
 

Related to Integral Help: Completing the square?

1. What is completing the square?

Completing the square is a mathematical method used to solve quadratic equations. It involves manipulating the equation to create a perfect square trinomial, which can then be easily solved using the quadratic formula or by factoring.

2. Why is completing the square useful?

Completing the square is useful because it allows us to solve quadratic equations that cannot be easily solved by factoring or using the quadratic formula. It is also used in calculus to find the minimum or maximum value of a quadratic function.

3. How do you complete the square?

To complete the square, follow these steps:

  1. Write the equation in the form ax² + bx + c = 0
  2. Divide both sides by a (the coefficient of x²) to make the coefficient of x² equal to 1.
  3. Move the constant term (c) to the right side of the equation.
  4. Take half of the coefficient of x (b) and square it. Add this value to both sides of the equation.
  5. Factor the perfect square trinomial on the left side and simplify the right side if needed.
  6. Take the square root of both sides and solve for x.

4. When should I use completing the square?

Completing the square should be used when solving a quadratic equation that cannot be easily factored or when the quadratic formula seems too complicated. It is also used in calculus to find the minimum or maximum value of a quadratic function.

5. Can completing the square be used for any type of quadratic equation?

Completing the square can be used for any quadratic equation in the form ax² + bx + c = 0, where a is not equal to 0. It cannot be used for equations with imaginary solutions.

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