Problem

Calculate the Riemann sum $R(f, P, C)$ for the function $f(x)=x$, the partition $P=\{1,1.3,1.7,2\}$, and the sample points $C=\{1.2,1.5,1.8\}$
(Use decimal notation. Give your answer to two decimal places.)
\[
R(f, P, C)=
\]

Answer

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Answer

Final Answer: The Riemann sum \(R(f, P, C)\) for the function \(f(x)=x\), the partition \(P=\{1,1.3,1.7,2\}\), and the sample points \(C=\{1.2,1.5,1.8\}\) is \(\boxed{1.5}\).

Steps

Step 1 :Define the function \(f(x) = x\).

Step 2 :Define the partition \(P = \{1, 1.3, 1.7, 2\}\) and the sample points \(C = \{1.2, 1.5, 1.8\}\).

Step 3 :Calculate the Riemann sum \(R(f, P, C)\) by summing up the product of the function evaluated at the sample points and the difference between consecutive partition points.

Step 4 :The Riemann sum \(R(f, P, C)\) for the function \(f(x)=x\), the partition \(P=\{1,1.3,1.7,2\}\), and the sample points \(C=\{1.2,1.5,1.8\}\) is calculated as 1.5.

Step 5 :Final Answer: The Riemann sum \(R(f, P, C)\) for the function \(f(x)=x\), the partition \(P=\{1,1.3,1.7,2\}\), and the sample points \(C=\{1.2,1.5,1.8\}\) is \(\boxed{1.5}\).

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