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Definite integrals (part II) Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Definite integrals (part II) Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is a definite integral? |  |
Ans. A definite integral is a mathematical concept that represents the accumulation of a quantity over a given interval. It is used to find the area under a curve, the displacement of an object, or the total value of a function within a specific range.
| 2. How is a definite integral different from an indefinite integral? | |
Ans. While both are types of integrals, the main difference lies in the inclusion of limits. A definite integral has upper and lower limits that define the interval over which the accumulation is calculated, whereas an indefinite integral represents the antiderivative of a function without any specified range.
| 3. What is the fundamental theorem of calculus and how does it relate to definite integrals? | |
Ans. The fundamental theorem of calculus states that if a function is continuous over a closed interval and has an antiderivative, then the definite integral of that function over the interval can be evaluated by subtracting the antiderivative at the upper limit from the antiderivative at the lower limit. This theorem provides a powerful tool for calculating definite integrals.
| 4. Can definite integrals be negative? | |
Ans. Yes, definite integrals can be negative. The sign of a definite integral depends on the behavior of the function being integrated over the given interval. If the function has negative values within the interval, the definite integral will yield a negative result. It represents the accumulated "net" quantity, taking into account both positive and negative contributions.
| 5. What are some practical applications of definite integrals? | |
Ans. Definite integrals have numerous applications in various fields. They are used to calculate areas, volumes, and lengths in geometry. In physics, definite integrals are employed to determine the total displacement, velocity, and acceleration of objects. They also find applications in economics, engineering, and computer science for modeling and analyzing real-world phenomena.
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