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. The cross-sections of the solid perpendicular to the x-axis are isosceles right triangles, as shown in the figure.**Which of the following integrals represents the volume of this solid?**- $\int_{a}^{b} \pi (f(x))^2 \, dx$- $\int_{a}^{b} \pi (f(x)) \, dx$- $\int_{a}^{b} (f(x))^2 \, dx$- $\int_{a}^{b} \frac{1}{2}(f(x))^2 \, dx$**Diagram Explanation:**The diagram illustrates the solid, where the region under the curve $ y = f(x) $ between $ x = a $ and $ x = b $ forms one side of the solid. Each slice perpendicular to the x-axis is shown as an isosceles right triangle, with the base and height equal to the value of $ f(x) $ at that slice. The volume of the solid is determined by integrating the area of these triangular slices along the interval $[a, b]$.

A solid is constructed so that one side is the region between the lines 0, 1= b, the graph of y = f(x) and the x-axis, and the cross- sections of the solid perpendicular to the x-axis are isosceles right triangles, as shown in the figure. Which of the following integrals represents the volume of this solid? S* n(f(x))² dæ b T(f(x)) dr [- f(f(=))² dz 4 Ba ½ (12))²2 de da y=f(x) each slice is a right triangle with base = height

A solid is constructed so that one side is the region between the lines 0, 1= b, the graph of y = f(x) and the x-axis, and the cross- sections of the solid perpendicular to the x-axis are isosceles right triangles, as shown in the figure. Which of the following integrals represents the volume of this solid? S* n(f(x))² dæ b T(f(x)) dr [- f(f(=))² dz 4 Ba ½ (12))²2 de da y=f(x) each slice is a right triangle with base = height

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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