What is the indefinite integral of {eq}\frac{2}{x}? {/eq}
Question:
What is the indefinite integral of {eq}\frac{2}{x}? {/eq}
Indefinite Integral:
An indefinite integral is an integral that does not have limits of integration. That is, we are not confining the integration interval only on a limited space. Instead, indefinite integrals usually evaluate the function from negative to positive infinity. Indefinite integrals also have an infinite number of solutions. Take the function {eq}\displaystyle f(x) = x {/eq} and {eq}\displaystyle g(x) = x + 10 {/eq}. These two functions are different yet they both have the same derivative of 1. The constant of integration allows us to account for constants which become zero during differentiation.
Answer and Explanation: 1
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Given the integral:
{eq}\displaystyle \int\ \frac{2}{x}\ dx {/eq}
We re-arrange this as:
{eq}\displaystyle \int\ \frac{2}{x}\ dx = 2\int\...
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Chapter 12 / Lesson 11Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.