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anyone could help to solve this problem,

so, i have the mathematical expression (shown in the picture below), the limit of integration for b is set in the range from 0 to 1, because the variation of b value, then the value of c(resut of integral) will be different for each b.

Plus, I am only allowed to use Simpson's rule to solve the integration. And the main goal of this task is getting the graph of f(c,b)

enter image description here

Mizuki Haruko
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You apply the quadrature rule cumulatively. That is, you apply Simpson quadrature to the intervals [0,0.01], [0.01,0.02], [0.02,0.03],... with the necessary evaluations of internal points to reach the required accuracy, scaled to the interval length, and then progressively sum up the single integral values to the integrals over the intervals [0, b], b=0.01, 0.02, 0.03,...

Lutz Lehmann
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