54 lines
1.1 KiB
Matlab
54 lines
1.1 KiB
Matlab
tic;
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samples = 100000;
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xBounds = LinearBounds(0,20);
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yBounds = LinearBounds(-10,150000);
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bounds = Bounds(xBounds,yBounds);
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pointsInside = 0;
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realValue = realIntegral(bounds.x);
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listOfErrors = [];
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listOfIntegrals = [];
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for i = 1:20
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for ii = 0:samples
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toTestPoint = bounds.getRandomPoint;
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if getIsInside(toTestPoint)
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pointsInside = pointsInside+1;
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end
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end
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listOfIntegrals(i) = pointsInside/samples*bounds.area;
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listOfErrors(i) = abs(listOfIntegrals(i) - realValue);
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pointsInside = 0;
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end
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format longG
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integral = (pointsInside/samples)*bounds.area
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realValue
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error = abs(realValue-integral)
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listOfErrors
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listOfIntegrals
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toc
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function out = mainFunction(x)
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out = x^4-4*x^3+18*x^2-12*x-69;
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end
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function out = indefiniteIntegral(x)
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out = (1/5)* x^5 - x^4 + 6* x^3 - 6*x^2 - 69*x;
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end
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function out = getIsInside(p)
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arguments
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p Point
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end
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y_0 = mainFunction(p.x);
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out = abs(y_0) > abs(p.y) && y_0 * p.y >= 0;
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end
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function out = realIntegral(bounds)
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arguments
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bounds LinearBounds
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end
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out = indefiniteIntegral(bounds.higher) - indefiniteIntegral(bounds.lower);
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end |