Setup the Riemann sum = [²³x²³ dx lim n→∞0 [(2+[(3*k)/n])^3]*(3/n) n Entered k=1 [*f(x) dx = f(x) dx = limf(x)Ax for the given integral. k=1 n→∞ (2+3k/n)^3*(3/n) n Answer Preview 3 3k 3 (2 + ³k ) ²2/1/2 n n
Setup the Riemann sum = [²³x²³ dx lim n→∞0 [(2+[(3*k)/n])^3]*(3/n) n Entered k=1 [*f(x) dx = f(x) dx = limf(x)Ax for the given integral. k=1 n→∞ (2+3k/n)^3*(3/n) n Answer Preview 3 3k 3 (2 + ³k ) ²2/1/2 n n
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Hey please solve thisc correctly.
(2+3k/n)^3*(3/n) this is not right answer. I want right answer
![The image contains a setup for evaluating a definite integral using Riemann sums.
**Entered:**
\[
[(2+[(3*k)/n])^3] \times (3/n)
\]
**Answer Preview:**
\[
\left(2 + \frac{3k}{n}\right)^3 \times \frac{3}{n}
\]
**Instructions:**
(a) Setup the Riemann sum for the given integral:
\[
\int_{a}^{b} f(x) \, dx = \lim_{n \to \infty} \sum_{k=1}^{n} f(\bar{x}_k) \Delta x
\]
**Example Integral:**
\[
\int_{2}^{5} x^3 \, dx = \lim_{n \to \infty} \sum_{k=1}^{n} \left(2 + 3k/n\right)^3 \times (3/n)
\]
This explains how to use Riemann sums to approximate the integral from 2 to 5 of the function \(x^3\). The expression inside the sum represents a function value at a sample point within each subinterval, multiplied by the width of the subinterval, \(\Delta x\). This sum approaches the definite integral as the number of subintervals, \(n\), approaches infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d5d9ef2-562b-49f4-9963-a1c4e47b1118%2F26485d87-469f-45eb-ae60-26c1b80e6b19%2Fwdx0g0h_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains a setup for evaluating a definite integral using Riemann sums.
**Entered:**
\[
[(2+[(3*k)/n])^3] \times (3/n)
\]
**Answer Preview:**
\[
\left(2 + \frac{3k}{n}\right)^3 \times \frac{3}{n}
\]
**Instructions:**
(a) Setup the Riemann sum for the given integral:
\[
\int_{a}^{b} f(x) \, dx = \lim_{n \to \infty} \sum_{k=1}^{n} f(\bar{x}_k) \Delta x
\]
**Example Integral:**
\[
\int_{2}^{5} x^3 \, dx = \lim_{n \to \infty} \sum_{k=1}^{n} \left(2 + 3k/n\right)^3 \times (3/n)
\]
This explains how to use Riemann sums to approximate the integral from 2 to 5 of the function \(x^3\). The expression inside the sum represents a function value at a sample point within each subinterval, multiplied by the width of the subinterval, \(\Delta x\). This sum approaches the definite integral as the number of subintervals, \(n\), approaches infinity.
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