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DavidLiew
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Homework Statement
How to approximate the [tex]\int[/tex] [tex]\int[/tex]e x2 dA where R is bounded by y=x2 and y=1.
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Mark44 said:There are any number of ways to approximate a definite integral. What have you tried so far?
Double integration is a mathematical technique used to find the area under a curve in a two-dimensional plane. It involves performing two integrals, one after the other, to approximate the total area bounded by the given curve.
In this specific case, double integration is used to find the area bounded by the curves y=x2 and y=1 in the region R. This involves integrating the function y=x2 with respect to x, from the lower bound (x=0) to the upper bound (x=1), and then integrating the result with respect to y, from the lower bound (y=0) to the upper bound (y=1).
R represents the region or area bounded by the given curves in a two-dimensional plane. It is the region for which we want to find the area using double integration.
Yes, double integration can be used to find the area of any region bounded by curves in a two-dimensional plane. However, the integration limits and the order of integration may vary depending on the specific region and curves.
One limitation of double integration is that it can only approximate the area bounded by curves, not provide an exact answer. Additionally, the process can become more complex for more complicated regions and curves, making it difficult to find the appropriate integration limits and order. Finally, double integration may not be suitable for regions that are not bounded by curves, such as irregular shapes or regions with holes.