Answer to Question #139332 in Calculus for Promise Omiponle

Question #139332
Calculate the double integral ∫∫R(8x+6y+48)dA where R is the region: 0≤x≤3,0≤y≤4.
1
Expert's answer
2020-10-26T20:00:01-0400

R(8x+6y+48)dA=0403(8x+6y+48)dxdy=04(4x2+6xy+48x)03dy=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}


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