b) Calculate again an approximate value of the length L of the curve arc from the previous paragraph, but now dividing the arc into four parts, as indicated in the following figure, and assuming, as before, that these four parts are segments straight. HOJA DE TRABAJO Consider y = y(x) = x リ= 4 3 2 3 2 a) Find an approximate value of the length L of the arc of the graph of y = x (x) = x2 from the point (0, and (0)) Until point (2, and (2)). To do this, divide the arch into two parts.as indicated in the following figure, and suppose that these two parts are line segments. トリ= 4. 3 2 1 2 3
b) Calculate again an approximate value of the length L of the curve arc from the previous paragraph, but now dividing the arc into four parts, as indicated in the following figure, and assuming, as before, that these four parts are segments straight. HOJA DE TRABAJO Consider y = y(x) = x リ= 4 3 2 3 2 a) Find an approximate value of the length L of the arc of the graph of y = x (x) = x2 from the point (0, and (0)) Until point (2, and (2)). To do this, divide the arch into two parts.as indicated in the following figure, and suppose that these two parts are line segments. トリ= 4. 3 2 1 2 3
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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Transcribed Image Text:**Worksheet:**
Consider \( y = y(x) = x^2 \).
### Graph of \( y = x^2 \):
The graph displays the function \( y = x^2 \) as a curved line in red. The horizontal axis is labeled \( x \), ranging from 0 to 3, and the vertical axis is labeled \( y \), ranging from 0 to 4.
### Task a:
a) Find an approximate value of the length \( L \) of the arc of the graph of \( y = y(x) = x^2 \) from the point (0, 0) until point (2, 4).
To do this, divide the arc into two parts, as indicated in the following figure, and suppose that these two parts are line segments.
#### Figure:
This is a graph of the function \( y = x^2 \), similar to the above, but with the arc divided into two line segments. The segments form a polyline approximation of the curve.
### Task b:
b) Calculate again an approximate value of the length \( L \) of the curve arc from Task a, but now dividing the arc into four parts, as indicated in the following figure, and assuming, as before, that these four parts are straight segments.
#### Figure:
This graph shows the function \( y = x^2 \) with the arc divided into four straight segments, further refining the polyline approximation of the curve.
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