Estimate the area under the graph of f(x) = x² + 1 [0, 3] using six approximating rectangles and right endpoints. R6 = Repeat the approximation using left endpoints. L6 over the interval = N 1.4 1.2 1 0/8- p.6+ 0.4+ 0.2 -1 -0.2- -0.4 1 2 3 4 Q
Estimate the area under the graph of f(x) = x² + 1 [0, 3] using six approximating rectangles and right endpoints. R6 = Repeat the approximation using left endpoints. L6 over the interval = N 1.4 1.2 1 0/8- p.6+ 0.4+ 0.2 -1 -0.2- -0.4 1 2 3 4 Q
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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![**Estimate the area under the graph of** \( f(x) = \frac{1}{x^2 + 1} \) **over the interval** \([0, 3]\) **using six approximating rectangles and right endpoints.**
\[ R_6 = \boxed{\phantom{\text{Answer here}}} \]
**Repeat the approximation using left endpoints.**
\[ L_6 = \boxed{\phantom{\text{Answer here}}} \]
**Graph Explanation:**
The graph to the right of the text displays the function \( f(x) = \frac{1}{x^2 + 1} \). It features a curve that starts from approximately \( (0, 0.5) \), peaks at \( (0, 1) \), and then decreases as \( x \) moves towards both negative and positive infinity. The graph is situated between the x-values of \(-2\) and \(5\) and y-values between \(-0.4\) and \(1.4\). The shape is symmetric around the y-axis, reflecting the even nature of the function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dd0957e-bb75-4f35-baf9-1596cc2b4cca%2F72d9f13c-581e-40f7-a5d1-56e1d6379e7d%2Ff6mxs9h_processed.png&w=3840&q=75)
Transcribed Image Text:**Estimate the area under the graph of** \( f(x) = \frac{1}{x^2 + 1} \) **over the interval** \([0, 3]\) **using six approximating rectangles and right endpoints.**
\[ R_6 = \boxed{\phantom{\text{Answer here}}} \]
**Repeat the approximation using left endpoints.**
\[ L_6 = \boxed{\phantom{\text{Answer here}}} \]
**Graph Explanation:**
The graph to the right of the text displays the function \( f(x) = \frac{1}{x^2 + 1} \). It features a curve that starts from approximately \( (0, 0.5) \), peaks at \( (0, 1) \), and then decreases as \( x \) moves towards both negative and positive infinity. The graph is situated between the x-values of \(-2\) and \(5\) and y-values between \(-0.4\) and \(1.4\). The shape is symmetric around the y-axis, reflecting the even nature of the function.
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