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Finding areas using integration, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com
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FAQs on Finding areas using integration, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. How can integration be used to find areas? |  |
Ans. Integration can be used to find areas by calculating the definite integral of a function over a given interval. The integral represents the area under the curve of the function within that interval. By evaluating this integral, we can find the exact numerical value of the area.
| 2. Can integration be used to find the area of irregular shapes? | |
Ans. Yes, integration can be used to find the area of irregular shapes. By dividing the irregular shape into smaller, regular shapes (such as rectangles or triangles), we can calculate the area of each shape using integration. Then, by summing up the areas of these smaller shapes, we can find the total area of the irregular shape.
| 3. What is the difference between indefinite and definite integration when finding areas? | |
Ans. Indefinite integration is used to find the antiderivative of a function, which represents a family of functions. It does not provide a specific numerical value for the area. On the other hand, definite integration is used to find the exact numerical value of the area under a curve. Definite integration involves specifying the limits of integration, which define the interval over which the area is to be calculated.
| 4. Can integration be used to find the area between two curves? | |
Ans. Yes, integration can be used to find the area between two curves. By finding the points of intersection between the two curves, we can determine the limits of integration. Then, by subtracting the integral of the lower curve from the integral of the upper curve, we can find the area between them.
| 5. Are there any limitations or assumptions when using integration to find areas? | |
Ans. Yes, there are some limitations and assumptions when using integration to find areas. One limitation is that integration assumes the function is continuous and well-behaved over the given interval. If the function has discontinuities or behaves irregularly, the calculated area may not be accurate. Additionally, integration assumes that the function is known or can be expressed as a mathematical formula. If the function is not known or cannot be expressed analytically, alternative methods may need to be used to estimate the area.
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Dec 23, 2024 Last updated |
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