The function y = f(x) is given by the figure. y = f(x) 1 0. 1 3. 4 6. -1 -2+ A(x) = f(t) dt B(x) = f(t) dt Find formulas for A(x) and B(x) valid on [4,5]. (Express numbers in exact form. Use symbolic notation and fractions where needed.) A(x) = B(x) =
The function y = f(x) is given by the figure. y = f(x) 1 0. 1 3. 4 6. -1 -2+ A(x) = f(t) dt B(x) = f(t) dt Find formulas for A(x) and B(x) valid on [4,5]. (Express numbers in exact form. Use symbolic notation and fractions where needed.) A(x) = B(x) =
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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![The function \( y = f(x) \) is given by the figure below.
[Graph Description]
- **Axes**: The graph is drawn on an \( xy \)-plane.
- **\( y = f(x) \)**: The function is represented as a piecewise graph:
- From \( x = 0 \) to \( x = 1 \), the graph linearly increases from \( y = 0 \) to \( y = 1 \).
- From \( x = 1 \) to \( x = 2 \), the linearly increases from \( y = 1 \) to \( y = 2 \).
- From \( x = 2 \) to \( x = 4 \), the graph is constant at \( y = 2 \).
- From \( x = 4 \) to \( x = 5 \), the graph linearly decreases from \( y = 2 \) to \( y = 0 \).
- From \( x = 5 \) to \( x = 6 \), the graph continues linearly decreasing from \( y = 0 \) to \( y = -2 \).
\[
A(x) = \int_{0}^{x} f(t) \, dt \quad \text{and} \quad B(x) = \int_{2}^{x} f(t) \, dt
\]
Find formulas for \( A(x) \) and \( B(x) \) valid on the interval \([4, 5]\).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
\[ A(x) = \underline{\hspace{15cm}} \]
\[ B(x) = \underline{\hspace{15cm}} \]
*Source: Rogawski 4e Calculus Early Transcendentals | Publisher: W.H. Freeman*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0a9522d-164b-4f9a-91f3-55e6c1137254%2F687540ba-de0c-4796-a25b-da4ac4dfbc6c%2Fick9k4f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The function \( y = f(x) \) is given by the figure below.
[Graph Description]
- **Axes**: The graph is drawn on an \( xy \)-plane.
- **\( y = f(x) \)**: The function is represented as a piecewise graph:
- From \( x = 0 \) to \( x = 1 \), the graph linearly increases from \( y = 0 \) to \( y = 1 \).
- From \( x = 1 \) to \( x = 2 \), the linearly increases from \( y = 1 \) to \( y = 2 \).
- From \( x = 2 \) to \( x = 4 \), the graph is constant at \( y = 2 \).
- From \( x = 4 \) to \( x = 5 \), the graph linearly decreases from \( y = 2 \) to \( y = 0 \).
- From \( x = 5 \) to \( x = 6 \), the graph continues linearly decreasing from \( y = 0 \) to \( y = -2 \).
\[
A(x) = \int_{0}^{x} f(t) \, dt \quad \text{and} \quad B(x) = \int_{2}^{x} f(t) \, dt
\]
Find formulas for \( A(x) \) and \( B(x) \) valid on the interval \([4, 5]\).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
\[ A(x) = \underline{\hspace{15cm}} \]
\[ B(x) = \underline{\hspace{15cm}} \]
*Source: Rogawski 4e Calculus Early Transcendentals | Publisher: W.H. Freeman*
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