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A solid is contructed so that one side is the region between the lines 2 = a, x= =b, the graph of y = f(x) and the x-axis, and the cross- sections of the solid perpendicular to the x-axis are rectangles with base 4 (as shown in the figure). Which of the following integrals represents the volume of this solid? [*4(f(x))² da of 47(f(x))² da of 4 f(a) de S* n(ƒ(2))² da y=f(x) each slice is a rectangle

A solid is contructed so that one side is the region between the lines 2 = a, x= =b, the graph of y = f(x) and the x-axis, and the cross- sections of the solid perpendicular to the x-axis are rectangles with base 4 (as shown in the figure). Which of the following integrals represents the volume of this solid? [*4(f(x))² da of 47(f(x))² da of 4 f(a) de S* n(ƒ(2))² da y=f(x) each slice is a rectangle

Advanced Engineering Mathematics
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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A solid is constructed so that one side is the region between the lines \( x = a \), \( x = b \), the graph of \( y = f(x) \) and the x-axis, and the cross-sections of the solid perpendicular to the x-axis are rectangles with base 4 (as shown in the figure). Which of the following integrals represents the volume of this solid? - \(\int_a^b 4(f(x))^2 \, dx\) - \(\int_a^b 4\pi(f(x))^2 \, dx\) - \(\int_a^b 4f(x) \, dx\) - \(\int_a^b \pi(f(x))^2 \, dx\) **Diagram Explanation:** The diagram illustrates a three-dimensional solid where the base is bounded by vertical lines at \( x = a \) and \( x = b \), and by the curve \( y = f(x) \) along with the x-axis. The cross-sections perpendicular to the x-axis form rectangles, each with a constant base of 4 units. The height of each rectangle is defined by the value of \( f(x) \) at that point, as depicted by a wave-like blue curve. The volume is calculated by integrating these rectangular cross-sections along the x-axis from \( a \) to \( b \).
Transcribed Image Text:A solid is constructed so that one side is the region between the lines \( x = a \), \( x = b \), the graph of \( y = f(x) \) and the x-axis, and the cross-sections of the solid perpendicular to the x-axis are rectangles with base 4 (as shown in the figure). Which of the following integrals represents the volume of this solid? - \(\int_a^b 4(f(x))^2 \, dx\) - \(\int_a^b 4\pi(f(x))^2 \, dx\) - \(\int_a^b 4f(x) \, dx\) - \(\int_a^b \pi(f(x))^2 \, dx\) **Diagram Explanation:** The diagram illustrates a three-dimensional solid where the base is bounded by vertical lines at \( x = a \) and \( x = b \), and by the curve \( y = f(x) \) along with the x-axis. The cross-sections perpendicular to the x-axis form rectangles, each with a constant base of 4 units. The height of each rectangle is defined by the value of \( f(x) \) at that point, as depicted by a wave-like blue curve. The volume is calculated by integrating these rectangular cross-sections along the x-axis from \( a \) to \( b \).
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table row y equals cell f open parentheses x close parentheses end cell row x equals a row x equals b end table 

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