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pythonfunctionareacurvesage
Martin
Martin

Reputation: 49

Determining the area of a closed curve in sagemath

Let's say I have the function y^(2) + x^(16) = 1 (represents a rounded square in R^2).

How can I determine the area of this (closed curve) function in sagemath (9.3)?

Integrals maybe?

Upvotes: 1

Views: 157

Answers (1)

Lisa
Lisa

Reputation: 66

SageMath provides integration functionality. Assuming that you want to find the area with this curve as boundary, you can do the following command in sagemath:

>>>4*integrate(sqrt(1-x^16),x,0,1)
1/4*beta(1/16, 3/2)

Explanation: Isolate y in the equation of your curve and integrate from 0 to 1. This will give you 1/4 of the total area bounded by this curve. Since the area is symmetric, you can multiply by 4 to get the area of the total "square".

Upvotes: 1

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