An electric charge is spread over a rectangular region $R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 4 \}$. Find the total charge on $R$ if the charge density at a point $( x , y )$ in $R$ (measured in coulombs per square meter $)$ is $\sigma ( x , y ) = x ^ { 2 } + 4 y ^ { 3 }$.
Select the correct answer.
A) 804 coulombs
B) 91 coulombs
C) 300 coulombs
D) 265 coulombs

Question

Quizplus · Accepted Answer

To find the total charge, integrate the charge density over the region $R$: $\int_{0}^{3} \int_{0}^{4} (x^2 + 4y^3) \, dy \, dx$. This evaluates to 804 coulombs.

An Electric Charge Is Spread Over a Rectangular Region R={(x,y)∣0≤x≤3,0≤y≤4}R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 4 \}R={(x,y)∣0≤x≤3,0≤y≤4}

An Electric Charge Is Spread Over a Rectangular Region $R = \{ ( x , y ) \mid 0 \leq x \leq 3,0 \leq y \leq 4 \}$