# 708 Centroid and area of spandrel by integration

# 707 Centroid of quarter ellipse by integration

# 706 Centroid of quarter circle by integration

# 705 Centroid of parabolic segment by integration

# Centroids and Centers of Gravity

Log in or Register to Discuss This!Center of gravity of a homogeneous flat plate
Centroids of areas
Centroids of lines
Center of gravity of bodies
Centroids of volumes

## Centroids of Composite Figures

$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$

$A \, \bar{x} = \Sigma ax$

$A \, \bar{y} = \Sigma ay$

$L \, \bar{x} = \Sigma lx$

$L \, \bar{y} = \Sigma ly$

## Center of Gravity of Bodies and Centroids of Volumes

$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$

$W \, \bar{z} = \Sigma wz$

$V \, \bar{x} = \Sigma vx$

$V \, \bar{y} = \Sigma vy$

$V \, \bar{z} = \Sigma vz$

# Example 7 | Area inside the square not common to the quarter circles

# 07 Area inside the larger circle but outside the smaller circle

# Infinite Series

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### Sequences and Series

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

$1,~ 8,~ 27,~ 64,~ 125,~ ...$

which is a sequence so that the n^{th} term is given by n^{3}.

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

$a_1 + a_2 + a_3 + ... + a_n + ...$

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

**Finite and Infinite Series**