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.
 

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.
 

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

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

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.
 

Problem
The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.
 

Problem
From the figure shown below, DE is the diameter of circle A and BC is the radius of circle B. If DE = 60 cm and AC = 10 cm, find the area of the shaded region.
 

Sequences and Series

Sequence is a succession of numbers formed according to some fixed rule. Example is

which is a sequence so that the n^th term is given by n³.
 

Series is the indicated sum of a sequence of numbers. Thus,

is the series corresponding to the sequence $a_1,~ a_2,~ a_3,~ ... ,~a_n,~ ...$
 

Finite and Infinite Series