Calculate the double integral ∫∫R (10x + 2y + 20 ) dA where R is the region: 0 ≤ x ≤ 1, 0 ≤ y ≤ 5.

Question

turingtest · Answer

$$\int\limits \int\limits10x+2y+20dA=\int\limits_{0}^{1}\int\limits_{0}^{5}10x-2y+20dydx$$$$=\int\limits_{0}^{1}10x(5)(5)^2+20(5)dx=\int\limits_{0}^{1}50xdx=25(1)^2=25$$

turingtest · Answer

sorry los a + sign on the second line, should be 10x(5)+(5)^2+20(5)

anonymous · Answer

yeah i was gonna say that !

turingtest · Answer

good, then you got it?

anonymous · Answer

yeah so its 175 !?

turingtest · Answer

wait a minute let me take it from where I messed up...

anonymous · Answer

ok

turingtest · Answer

argh! it's 150
stupid thing, want me to show it from the top?

turingtest · Answer

the program can be stupid I mean...

anonymous · Answer

ok cause now i'm lost !

anonymous · Answer

i understand  !

turingtest · Answer

$$\int\limits_{0}^{1}\int\limits_{0}^{5}10x+2y+20dydx=\int\limits_{0}^{1}10x(5)+5^2+20(5)dx$$$$\int\limits_{0}^{1}50x+125dx=25+125=50$$

turingtest · Answer

see that, the last line is clearly 25+125=150
there is a delay, sorry for the confusion.

anonymous · Answer

yeah thanks ! i actually did it myself but thanks for all the explanations !