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Standard forms of Integration, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com
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FAQs on Standard forms of Integration, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. What is the standard form of integration? |  |
Ans. The standard form of integration refers to the basic format or structure used to represent an integral. In calculus, it is commonly represented as ∫f(x)dx, where f(x) is the function being integrated and dx represents the differential of x.
| 2. How is integration used in business mathematics? | |
Ans. Integration plays a crucial role in business mathematics as it helps in solving various real-world problems. It is used to determine the total cost, revenue, and profit functions, calculate the area under a curve representing demand or supply, analyze growth rates, and make predictions based on mathematical models.
| 3. What are the different techniques used in integration? | |
Ans. There are several techniques used in integration, including:
1. Integration by substitution: This technique involves substituting a variable or expression with a new variable to simplify the integral.
2. Integration by parts: This method is used when the integral of a product of two functions is difficult to solve. It involves applying the product rule of differentiation in reverse.
3. Partial fraction decomposition: This technique is used to decompose a rational function into simpler fractions, making it easier to integrate.
4. Trigonometric substitution: It involves substituting trigonometric functions to simplify the integral.
5. Integration by trigonometric identities: This method utilizes trigonometric identities to rewrite the integral in a form that can be easily solved.
| 4. How can integration be applied in statistics? | |
Ans. Integration is used in statistics to calculate probabilities and cumulative distribution functions. It helps in determining the area under probability density functions, which gives the probability of a random variable falling within a certain range. Integration is also employed in regression analysis, where it is used to estimate regression coefficients and evaluate the goodness of fit for statistical models.
| 5. Can integration be used to find the average of a set of data? | |
Ans. No, integration is not typically used to find the average of a set of data. The average, or mean, of a set of data is usually computed by summing all the values and dividing by the total number of values. Integration, on the other hand, is used to find the area under a curve or to calculate the total accumulation of a quantity over a given interval. While integration can be used in certain statistical calculations, finding the average is not one of them.
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Dec 23, 2024 Last updated |
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