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Integrals Class 12 Notes Maths Chapter 7

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FAQs on Integrals Class 12 Notes Maths Chapter 7

1. What is the basic definition of an integral?
Ans. An integral is a mathematical concept used to calculate the area under a curve or the accumulation of a quantity over an interval. It is denoted by the symbol ∫ and is an important concept in calculus.
2. What is the difference between a definite and indefinite integral?
Ans. A definite integral has specific limits of integration and gives a numerical value as a result. It represents the accumulated value of a function over a given interval. On the other hand, an indefinite integral does not have specific limits and gives a general function as a result, representing a family of functions that have the same derivative.
3. How can integrals be used to find the area under a curve?
Ans. Integrals can be used to find the area under a curve by calculating the definite integral of the function over a specific interval. The result of the definite integral represents the area between the curve and the x-axis within that interval.
4. What are the different methods for evaluating integrals?
Ans. There are several methods for evaluating integrals, including: 1. Direct integration: This involves finding the antiderivative of a function and using it to evaluate the integral. 2. Integration by substitution: This method involves substituting a new variable to simplify the integral. 3. Integration by parts: This method is used when the integral of a product of two functions needs to be evaluated. 4. Partial fraction decomposition: This method is used to break down a rational function into simpler fractions for easier integration.
5. What are some applications of integrals in real-life situations?
Ans. Integrals have numerous applications in various fields, including: 1. Physics: Integrals are used to calculate quantities such as work, energy, and electric field strength. 2. Engineering: Integrals are used in the analysis of structures, fluid flow, and electrical circuits. 3. Economics: Integrals are used to model and analyze economic functions, such as supply and demand curves. 4. Probability and statistics: Integrals are used to calculate probabilities and expected values in probability theory and statistical analysis. 5. Medicine: Integrals are used in medical imaging techniques, such as computed tomography (CT) scans, to reconstruct images from data obtained through scans.
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