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Geometric Interpretation of Definite Integral Video Lecture | Mathematics for Competitive Exams

FAQs on Geometric Interpretation of Definite Integral Video Lecture - Mathematics for Competitive Exams

1. What is the geometric interpretation of a definite integral?

Ans. The geometric interpretation of a definite integral is that it represents the signed area between the graph of a function and the x-axis over a specific interval.

2. How is the geometric interpretation of a definite integral related to finding area?

Ans. The geometric interpretation of a definite integral relates to finding area because the definite integral calculates the signed area under a curve. It can be used to find the area of irregular shapes by breaking them down into infinitesimally small rectangles and summing up their areas.

3. Can the geometric interpretation of a definite integral be negative?

Ans. Yes, the geometric interpretation of a definite integral can be negative. If the curve lies below the x-axis over the given interval, the definite integral will yield a negative value, indicating that the area is subtracted from the total.

4. How can the geometric interpretation of a definite integral be used to calculate displacement?

Ans. The geometric interpretation of a definite integral can be used to calculate displacement by considering the graph of a velocity function. The definite integral of the velocity function over a specific time interval represents the net change in position or displacement during that interval.

5. Can the geometric interpretation of a definite integral be extended to three dimensions?

Ans. Yes, the geometric interpretation of a definite integral can be extended to three dimensions. In this case, the definite integral represents the signed volume between the graph of a function and a plane or between two graphs of functions over a specific region in space.

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Oct 14, 2025 Last updated

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