Answer:
The total charge on the rectangle is 29.33C
Step-by-step explanation:
Given
σ(x, y) = 2xy + y²
For 2 ≤ x ≤ 4, 0 ≤ y ≤ 2
The total charge on the rectangle is calculated as follows.
Charge, q = ∫∫2xy + y² dydx {0,2}{2,4}
Integrate with respect to y
q = ∫xy² + ⅓y³ dydx {0,2}{2,4}
q = ∫(2²*x + ⅓*2³) dx {2,4}
q = ∫4x + 8/3 dx {2,4}
Integrate with respect to x
q = 2x² + 8x/3 {2,4}
q = (2(4)² + 8(4)/3) - (2(2)² + 8(2)/3)
q = 29.33C
