∬R(8x+6y+48) dA=∫04∫03(8x+6y+48) dx dy=∫04(4x2+6xy+48x) ∣03 dy=∫04(36+18y+144) dy=∫04(180+18y) dy=(180y+9y2)∣04=720+144=864\begin{aligned} \iint_R (8x + 6y + 48)\, \mathrm{d}A&= \int_0^4 \int_0^3 (8x + 6y + 48)\, \mathrm{d}x\, \mathrm{d}y\\ &=\int_0^4 (4x^2 + 6xy + 48x)\, \vert_0^3 \, \mathrm{d}y\\ &= \int_0^4 (36 + 18y + 144)\, \mathrm{d}y \\ &= \int_0^4 (180 + 18y)\, \mathrm{d}y \\&= (180y + 9y^2)\vert_0^4 \\&= 720 + 144 = 864 \end{aligned}∬R(8x+6y+48)dA=∫04∫03(8x+6y+48)dxdy=∫04(4x2+6xy+48x)∣03dy=∫04(36+18y+144)dy=∫04(180+18y)dy=(180y+9y2)∣04=720+144=864
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