Vertical Strip

Area, moment of inertia, and radius of gyration of parabolic section

Situation
Given the parabola 3x2 + 40y – 4800 = 0.
 

Part 1: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit2
B. 8 300 unit2
C. 5 600 unit2
D. 6 400 unit2
 

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit4
B. 18 362 000 unit4
C. 11 100 000 unit4
D. 21 065 000 unit4
 

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units
 

709 Centroid of the area bounded by one arc of sine curve and the x-axis

Problem 709
Locate the centroid of the area bounded by the x-axis and the sine curve $y = a \sin \dfrac{\pi x}{L}$ from x = 0 to x = L.
 

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

 

707 Centroid of quarter ellipse by integration

Problem 707
Determine the centroid of the quadrant of the ellipse shown in Fig. P-707. The equation of the ellipse is $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$.
 

Centroid of quarter ellipse in the first quadrant

 

706 Centroid of quarter circle by integration

Problem 706
Determine the centroid of the quarter circle shown in Fig. P-706 whose radius is r.
 

Centroid of quarter circle

 

705 Centroid of parabolic segment by integration

Problem 705
Determine the centroid of the shaded area shown in Fig. P-705, which is bounded by the x-axis, the line x = a and the parabola y2 = kx.
 

Open to the right parabola in the first quadrant

 

Example 6 | Plane Areas in Rectangular Coordinates

Example 6
Find each of the two areas bounded by the curves y = x3 - 4x and y = x2 + 2x.
 

Example 5 | Plane Areas in Rectangular Coordinates