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# Integrate the function $\frac{1}{x^2}$ from $-2$ to $1$

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##  Final answer to the problem

The integral diverges.

##  Step-by-step Solution 

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• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

Since the integral $\int_{-2}^{1}\frac{1}{x^2}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{-2}^{0}\frac{1}{x^2}dx+\int_{0}^{1}\frac{1}{x^2}dx$

Learn how to solve limits to infinity problems step by step online.

$\int_{-2}^{0}\frac{1}{x^2}dx+\int_{0}^{1}\frac{1}{x^2}dx$

Learn how to solve limits to infinity problems step by step online. Integrate the function 1/(x^2) from -2 to 1. Since the integral \int_{-2}^{1}\frac{1}{x^2}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{-2}^{0}\frac{1}{x^2}dx results in: \lim_{c\to0}\left(\frac{1}{-c}-\frac{1}{2}\right). The integral \int_{0}^{1}\frac{1}{x^2}dx results in: \lim_{c\to0}\left(-1+\frac{1}{c}\right). Gather the results of all integrals.

##  Final answer to the problem

The integral diverges.

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

###  Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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