Considering uniform partitions of n subintervals, find the Riemann sums (E=1f(Cx)Axx). Where C is the midpoint of the interval [xx-1, X] or the point cx € [Xx-1, Xx] that satisfies: f(xx-1) + f(Xx) f(Cx) 2 and f(x) = x2; [a,b] = [-2,0]. Also, find lim =1f(C;)4xx n-00

Q: Let f(x) = x² – 1 for r in [-2,2], and let P = {-2,1,2} be a partition of [-2, 2]. Find the upper…

A: The solution are next step is

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A: It is given that Q  is a refinement of P. Let P=I1,I2,I3…,In be the partition of a,b. Thus, Mk=sup…

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A:

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A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

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A: Given: fx=x+2x+1xx-13x-2. Also, the intervals are: (a) -3, 2.5     (b) -2.5, 3     (c) -1.75, 1.5…

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A:

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A: Please refer the attached image for complete solution. THANK YOU.

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A: From maximum value and minimum value in the corresponding intervals from that we can easily solve.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.