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Homework Statement
∫-∞∞(dx/x2)
Homework Equations
The Attempt at a Solution
∫(dx/x2) = -1/x
(-1/∞) - (-1/-∞) = 0
However, the answer is that the integral diverges. Why is this the case?
An improper integral is a type of definite integral where one or both of the limits of integration are infinite or the integrand has a vertical asymptote within the interval of integration. It is also known as a divergent integral.
To determine if an improper integral converges, you can use the limit comparison test, the comparison test, the integral test, or the ratio test. These tests involve comparing the given integral to a known convergent or divergent integral.
Yes, improper integrals can converge to a specific value if the integral is convergent. However, if the integral is divergent, it does not have a specific value.
If both limits of integration are infinite, the integral is called a double improper integral. To determine if a double improper integral converges, you can use the same tests as for a single improper integral.
Yes, improper integrals are commonly used in physics and engineering to solve problems involving infinite quantities, such as calculating the work done by a variable force or finding the center of mass of an object with an infinite density function.