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Methods of Integration, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com
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FAQs on Methods of Integration, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. What are the basic methods of integration? |  |
Ans. The basic methods of integration include the power rule, substitution, integration by parts, partial fractions, and trigonometric substitution. These methods are used to find the antiderivative or integral of a function.
| 2. How does the power rule work in integration? | |
Ans. The power rule states that if the integral of x raised to the power of n is desired, the resulting integral will be (x^(n+1))/(n+1), where n is any real number except -1. This rule allows us to find the integral of functions that are powers of x.
| 3. What is substitution in integration and how does it work? | |
Ans. Substitution is a method used to simplify integrals by making a substitution of variables. It involves replacing the variable in the integral with a new variable that will simplify the integral. This is done by choosing an appropriate substitution that will transform the integral into a simpler form, which can then be easily evaluated.
| 4. How does integration by parts work? | |
Ans. Integration by parts is a method used to find the integral of a product of two functions. It is based on the product rule of differentiation. The formula for integration by parts is ∫(u dv) = uv - ∫(v du), where u and v are functions of x and du and dv represent their differentials. This method is useful when the integral of a product is difficult to evaluate directly.
| 5. What is the purpose of partial fractions in integration? | |
Ans. Partial fractions is a technique used to simplify the integration of rational functions. It involves decomposing a rational function into a sum of simpler fractions called partial fractions. This allows us to break down a complex integral into simpler integrals that can be evaluated more easily. Partial fractions are particularly useful when dealing with rational functions that contain polynomial factors.
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Dec 23, 2024 Last updated |
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