Determine by integration the centroid (?̅) of theshape in the figure (to the right). The image illustrates a region bounded by the curve \( y^2 = 3x \), an equation representing a parabola that opens to the right. This region is shaded in pink. The graph is plotted on the Cartesian plane with the x-axis and y-axis clearly marked. The region of interest extends from the origin to the point where \( x = 6 \). At this point, a vertical line is drawn up to intersect the curve. The vertical line at \( x = 6 \) has a height of 4.24 units, indicating the upper bound of the region along the y-axis.Key elements to note:- The equation \( y^2 = 3x \) characterizes the parabolic curve.- The x-axis is labeled with an extension from 0 to 6 units.- The height of the region at \( x = 6 \) is marked as 4.24 units.This diagram serves as a visual representation of the area under the curve \( y^2 = 3x \), between \( x = 0 \) and \( x = 6 \).

Answered: Determine by integration the centroid…

Engineering

Civil Engineering

Determine by integration the centroid (?̅) of the shape in the figure (to the right).

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Graphical Methods

The graphical method is a method of solving equations involving more than one variable using the Cartesian coordinate system. In civil engineering, the use of the graphical method is limited to the problems involving two variables. The graphical method has a great impact in solving the questions regarding engineering mechanics.

Question

Determine by integration the centroid (?̅) of the
shape in the figure (to the right).

The image illustrates a region bounded by the curve \( y^2 = 3x \), an equation representing a parabola that opens to the right. This region is shaded in pink. The graph is plotted on the Cartesian plane with the x-axis and y-axis clearly marked.

The region of interest extends from the origin to the point where \( x = 6 \). At this point, a vertical line is drawn up to intersect the curve. The vertical line at \( x = 6 \) has a height of 4.24 units, indicating the upper bound of the region along the y-axis.

Key elements to note:
- The equation \( y^2 = 3x \) characterizes the parabolic curve.
- The x-axis is labeled with an extension from 0 to 6 units.
- The height of the region at \( x = 6 \) is marked as 4.24 units.

This diagram serves as a visual representation of the area under the curve \( y^2 = 3x \), between \( x = 0 \) and \( x = 6 \).

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