Solving the Integral of 1/x^2: A Quick Guide for Scientists

  • Thread starter kasse
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In summary, the formula for solving Int(1/x^2) is ∫ 1/x^2 dx = -1/x + C, and the power rule cannot be used for this integral. The domain of the integral is all real numbers except 0, and one way to simplify it is by rewriting it as ∫ x^-2 dx. A graph of 1/x^2 can help understand the integral, which represents the area under the curve from a given point to infinity.
  • #1
kasse
384
1
How do I solve that one?
 
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  • #2
Do you know how to integrate x^n ?
 
  • #3
And what is n in this problem?
 
  • #4
I see, lol. Stupid thinking.
 

1. What is the formula for solving Int(1/x^2)?

The formula for solving Int(1/x^2) is ∫ 1/x^2 dx = -1/x + C, where C is a constant of integration.

2. Can Int(1/x^2) be solved using the power rule?

No, the power rule only applies to integrals of the form ∫ x^n dx, where n is a constant. Since the exponent in this integral is -2, the power rule cannot be used.

3. What is the domain of the integral Int(1/x^2)?

The domain of this integral is all real numbers except 0, as the function 1/x^2 is undefined at x=0.

4. How can I simplify Int(1/x^2) before solving it?

One way to simplify this integral is by using the property of exponents that states x^-2 = 1/x^2. This allows us to rewrite the integral as ∫ x^-2 dx, which may be easier to integrate.

5. Is there a graph that can help me understand Int(1/x^2)?

Yes, the graph of 1/x^2 is a hyperbola with a vertical asymptote at x=0. The integral of this function is the area under the curve from a given point to infinity, which approaches 0 as the limit of integration approaches infinity.

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