Jawab:

massa: 20

Pusat massa: (3/5, 0)

Penjelasan dengan langkah-langkah:

Massa Lamina:

m = ∫∫_D [ δ(x,y) ] dA

= ∫∫_(0 ≤ x ≤ 1, −2 ≤ y ≤ 2) [6x + 2] dydx

= ∫∫_(0 ≤ x ≤ 1, −2 ≤ y ≤ 2) [y(6x + 2)] dx

= ∫_(0 ≤ x ≤ 1) [24x + 8]dy

= 20

Momen dari lamina sepanjang sumbu x:

m_x = ∫∫_D [y(δ(x,y)) ] dA

m_x = ∫∫_(0 ≤ x ≤ 1, −2 ≤ y ≤ 2) [y(6x + 2) ] dydx

m_x = 0

Momen dari lamina sepanjang sumbu y:

m_y = ∫∫_D [x(δ(x,y)) ] dA

m_y = ∫∫_(0 ≤ x ≤ 1, −2 ≤ y ≤ 2) [x(6x + 2) ] dydx

m_y = ∫∫_(0 ≤ x ≤ 1) [ 24x² + 8x] dydx

m_y = 12

Pusat Massa lamina tersebut adalah

X = m_y/m = 12/20 = 3/5

Y = m_x/m = 0/20 = 0