Solving Integral Problem: x(x2-4)1/2dx

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In summary, the conversation is about solving the integral \intx(x2-4)1/2dx. The person is having trouble finding the correct method to solve it and has tried integration by parts without success. Another person suggests using the substitution y=x2-4 and integrating (y1/2)/2, which should be easier. The conversation ends with the person realizing they should use u substitution to solve the integral.
  • #1
evilq17
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I am having problems figuring out how to do this integral.
[tex]\int[/tex]x(x2-4)1/2dx

I know what the answer is, but I am not sure how to get there. I am not sure if there is a method or if you just need to do it by logic. I tried integration by parts but I just can't get to something I can integrate.

Thanks.
 
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  • #2
try y=x2-4. Then dy=2xdx. Now you are left with integrating (y1/2)/2. You should be able to do that.
 
  • #3
You probably COULD do it by parts? But that's clearly overkill. Like mathman pointed out, this screams u-subst.
 
  • #4
Thanks. U substitution. Its been too long since I have done this. Thanks.
 

FAQ: Solving Integral Problem: x(x2-4)1/2dx

What is an integral problem?

An integral problem involves finding the area under a curve on a graph. It is a way of calculating the total value of a function over a specific interval.

What is the formula for solving an integral problem?

The formula for solving an integral problem is ∫f(x)dx = F(x) + C, where f(x) is the function to be integrated, F(x) is the antiderivative of f(x), and C is the constant of integration.

How do you solve a definite integral problem?

To solve a definite integral problem, you need to evaluate the antiderivative of the function at the upper and lower limits of the integration, and then subtract the lower limit from the upper limit.

What is the power rule for solving an integral problem?

The power rule states that the integral of x^n is (x^(n+1))/(n+1) + C, where n is any real number except for -1.

Can you use substitution to solve an integral problem?

Yes, substitution is a common technique used to solve integral problems. It involves substituting a variable in the function with a new variable to make the integration easier.

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