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anonymous
 4 years ago
When the integral g(x) from 2 to 5 is equal to 5. What is the integral from 2 to 5 of (g(x)+2)dx=? I thought it would be 7, but the teacher as an answer of 19. Please explain thought process.
anonymous
 4 years ago
When the integral g(x) from 2 to 5 is equal to 5. What is the integral from 2 to 5 of (g(x)+2)dx=? I thought it would be 7, but the teacher as an answer of 19. Please explain thought process.

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hartnn
 4 years ago
Best ResponseYou've already chosen the best response.0the integral, gets distributed to both terms. \[\int g(x)dx+\int 2 dx\] so, you need to solve 2nd integral separately, [1st integral=5] can you ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i just did the same, but i didn't get 19...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@hartnn i did that but got 11. unless the 2 becomes a positive 2 somehow, i don't see how you get 19.

phi
 4 years ago
Best ResponseYou've already chosen the best response.0what is \[2\int\limits_{2}^{5}dx\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0YUP! come on and say int dude: "F that teacher!"

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The teacher is right though?

whpalmer4
 4 years ago
Best ResponseYou've already chosen the best response.3If you think of the integral definition, it's just summing up the little rectangles under the curve. In the attached figure, the light blue area is g(x) integrated from x = 2 to x = 5, and has area = l*w = 7*(5/7) = 5. When we switch to integrating g(x) + 2 over that same portion of the x axis, we add in the green region, and now our area is increased by the area l*w = 2*7 = 14, giving a total of 5+14 = 19.

whpalmer4
 4 years ago
Best ResponseYou've already chosen the best response.3Sorry, bad label in my graph, g(x) = 5/7, not 5x/7!

ZeHanz
 4 years ago
Best ResponseYou've already chosen the best response.0@IStutts : although teachers sometimes make mistakes (I know, because I am a teacher), in this case the teacher's right, just read @whpalmer4's answer...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hartnn's description makes the most sense to me mathmatically. Thanks for the help!! :)
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