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Fundamental Theorem of Calculus- 1 Video Lecture | Mathematics for Competitive Exams
FAQs on Fundamental Theorem of Calculus- 1 Video Lecture - Mathematics for Competitive Exams
| 1. What is the Fundamental Theorem of Calculus? |  |
Ans. The Fundamental Theorem of Calculus is a fundamental result in calculus that establishes the relationship between differentiation and integration. It states that if a function is continuous on a closed interval, then the integral of its derivative over that interval is equal to the difference between the values of the function at the endpoints of the interval.
| 2. How is the Fundamental Theorem of Calculus applied in mathematics? | |
Ans. The Fundamental Theorem of Calculus is applied in various ways in mathematics. It allows us to evaluate definite integrals by finding antiderivatives of functions and then evaluating them at the endpoints of the interval. It also provides a method for calculating areas under curves and solving problems involving rates of change.
| 3. Can the Fundamental Theorem of Calculus be used to find indefinite integrals? | |
Ans. Yes, the Fundamental Theorem of Calculus can be used to find indefinite integrals. By applying the theorem, we can find the antiderivative of a function and evaluate it at a specific point to find the value of the indefinite integral.
| 4. What are the prerequisites for understanding the Fundamental Theorem of Calculus? | |
Ans. To understand the Fundamental Theorem of Calculus, it is important to have a solid understanding of basic calculus concepts, including limits, derivatives, and integrals. Knowledge of the chain rule, product rule, and power rule for differentiation is also necessary.
| 5. Are there any real-world applications of the Fundamental Theorem of Calculus? | |
Ans. Yes, the Fundamental Theorem of Calculus has numerous real-world applications. It is used in physics to calculate quantities such as displacement, velocity, and acceleration. It is also used in economics to model and analyze various economic phenomena, such as supply and demand functions and consumer surplus. Additionally, it is applied in engineering to solve problems related to motion, fluid dynamics, and electrical circuits.
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