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Integrate. -1/x^2

  Integrate-1/x^2 To integrate the function -1/x^2, you can use the power rule for integration. The power rule states that ∫x^n dx = (x^(n+1))/(n+1), where n ≠ -1. Applying the power rule, we can rewrite -1/x^2 as -x^(-2). Integrating -x^(-2), we get: ∫(-1/x^2) dx = ∫(-x^(-2)) dx Using the power rule, the integral becomes: = -x^(-2 + 1)/(2 - 1) + C = -x^(-1)/1 + C = -1/x + C Therefore, the integral of -1/x^2 is -1/x + C, where C is the constant of integration.
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What are rational number in mathematics

 What are rational numbers? A rational number is a number that can be expressed as a ratio of two integers. In other words, it is a number that can be written in the form of a fraction, where the numerator and denominator are both integers. For example, 2/3, 7/4, and -5/6 are all rational numbers. Rational numbers are an important concept in mathematics, and they have many useful properties. In this article, we will explain what rational numbers are, how they are used in mathematics, and some of their key properties. What are Rational Numbers? A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. For example, the number 2/3 is a rational number because it can be expressed as the ratio of the integers 2 and 3. Similarly, the number -5/6 is a rational number because it can be expressed as the ratio of the integers -5 and 6. Rational numbers are a subset of the real numbers, which includes all numbers that can be represented...
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What is integer with example

  What is integer with example  An integer is a whole number that does not have a fraction or decimal part. It is a number that can be represented without using any fractions, decimals, or mixed numbers.  Integers include positive numbers, negative numbers, and zero. Positive integers are numbers greater than zero, while negative integers are numbers less than zero. Zero is neither positive nor negative.  Here are some examples of integers: - 5 - -3 - 0 - 100 - -987 - 1,000,000 Integers can be used in many different mathematical operations, such as addition, subtraction, multiplication, and division. For example, if you add 2 and 3, you get 5, which is an integer. Similarly, if you subtract 3 from 10, you get 7, which is also an integer. Integers are used in many different areas of mathematics, including algebra, geometry, and calculus. They are also used in everyday life, such as when counting objects or calculating distances. It is important to understand the conce...
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What is energy in physics.

  What is energy? explain. Energy is a fundamental concept in physics that describes the ability of a system to do work. It is a scalar quantity that is conserved in most physical processes. The concept of energy is central to our understanding of the physical world and is used to describe everything from the behavior of subatomic particles to the movements of the galaxies. In this article, we will provide a detailed explanation of energy in physics, covering its definition, types, and applications. Definition of Energy In physics, energy is defined as the ability to do work. Work, in turn, is defined as the application of a force over a distance. Energy can exist in many different forms, including kinetic energy, potential energy, thermal energy, electromagnetic energy, and nuclear energy. Kinetic Energy Kinetic energy is the energy of motion. It is the energy an object possesses due to its motion. Kinetic energy is calculated using the formula: KE = 1/2 mv² Where KE is the ...
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What is abnormal molar mass

  Abnormal molar mass  Molar mass is the mass of one mole of a substance, which is expressed in grams per mole. It is a fundamental property of matter that is used to calculate various chemical quantities. However, in some cases, the molar mass of a substance can deviate from its expected value. This deviation is known as an abnormal molar mass, and it can be caused by a variety of factors. In this article, we will explore the concept of abnormal molar mass in detail, including its causes, effects, and applications. Abnormal molar mass can occur in several ways. One common cause is the presence of isotopes. Isotopes are atoms of the same element that have a different number of neutrons in their nuclei. This results in a different atomic mass for each isotope. When a substance contains isotopes, its molar mass will be different from the mass of a single atom or molecule. Another cause of abnormal molar mass is the presence of impurities. Impurities are substances that are not p...
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What is the difference between resistance and resistivity in physics.

  What is the difference between resistance and resistivity . In physics, resistance and resistivity are two important concepts that are related to the flow of electrical current through a material. While these terms are often used interchangeably, they actually have different meanings. Resistance is a measure of how much a material opposes the flow of electrical current. It is defined as the ratio of the voltage across a material to the current flowing through it, and is measured in ohms (Ω). Resistance depends on the physical properties of the material, including its size, shape, and composition, as well as the temperature and other environmental factors. Materials with high resistance are called insulators, while those with low resistance are called conductors. On the other hand, resistivity is a fundamental property of a material that describes how well it conducts electricity. Resistivity is defined as the resistance of a material with a unit length and unit cross-sectional ar...
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What is electric potential?

 What is electric potential? Physics class 12 Electric potential, in simple language, refers to the amount of electric potential energy possessed by a charged object per unit of electric charge. It represents the electrical "pressure" or "force" experienced by a charged particle at a particular location in an electric field. Think of electric potential as similar to gravitational potential. Just as a ball placed at a higher elevation has gravitational potential energy due to its position, a charged object has electric potential energy due to its position in an electric field. The electric potential is a measure of how much electric potential energy per unit charge is stored at a specific point. Electric potential is measured in volts (V), named after the Italian physicist Alessandro Volta. It can be thought of as the "push" or "pull" that charged particles experience within an electric field. When an electric charge is placed in an area of high e...
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Difference between electric field and electric potential

 Difference between electric field and electric potential. Electric field and electric potential are two fundamental concepts in electromagnetism that describe different aspects of the behavior of electric charges. Here's a breakdown of their differences: Electric Field: 1. Definition: The electric field at a given point in space is a vector quantity that describes the force experienced by a positive test charge placed at that point. 2. Cause: Electric fields are created by electric charges. A charged object generates an electric field around itself, and other charges in the vicinity experience a force due to this field. 3. Direction and Magnitude: Electric fields have both direction and magnitude. The direction of the electric field at a point is the direction in which a positive test charge would move if placed at that point. The magnitude of the electric field is the force experienced per unit positive test charge. 4. Units: The SI unit of electric field is newtons per coulomb (...
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Mi vs Csk

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 Clash of Titans: MI vs CSK IPL 2024 Showdown** The Indian Premier League (IPL) 2024 witnessed a thrilling clash between two cricketing powerhouses, the Mumbai Indians (MI) and the Chennai Super Kings (CSK). As fans across the globe tuned in, the match lived up to its hype, delivering a spectacle filled with drama, passion, and outstanding performances. **1. Rivalry Renewed:** The MI vs CSK rivalry has become one of the most intense and celebrated rivalries in IPL history. With multiple titles between them, each match between these two teams is eagerly anticipated by fans, and IPL 2024 was no exception. **2. Battle of the Titans:** Both teams boast a star-studded lineup, featuring some of the best players in the world. From the explosive batting of Rohit Sharma and Suryakumar Yadav for MI to the ever-reliable MS Dhoni and Faf du Plessis for CSK, the stage was set for a showdown of epic proportions. **3. The Match:** In a high-scoring encounter, MI won the toss and elected to bat fi...
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What is capacitor in simple language .

 What is capacitor basic information A capacitor is an electronic component that stores and releases electrical energy. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is created, causing the accumulation of electric charges on the plates. This charge separation allows the capacitor to store energy in the electric field. Capacitors are commonly used in electronic circuits for various purposes, such as filtering, energy storage, timing, and coupling signals between different parts of a circuit.
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