spandrel

708 Centroid and area of spandrel by integration

Problem 708
Compute the area of the spandrel in Fig. P-708 bounded by the x-axis, the line x = b, and the curve y = kxn where n ≥ 0. What is the location of its centroid from the line x = b? Determine also the y coordinate of the centroid.
 

Centroid and area of spandrel under the curve y = kx^n

 

Example 4 | Plane Areas in Rectangular Coordinates

Example 4
Solve the area bounded by the curve y = 4x - x2 and the lines x = -2 and y = 4.
 

Example 2 | Plane Areas in Rectangular Coordinates

Example 2
Find the area bounded by the curve a2 y = x3, the x-axis and the line x = 2a.
 

Moment Diagram by Parts

The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

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