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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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the 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 ?
i just did the same, but i didn't get 19...
@hartnn i did that but got 11. unless the -2 becomes a positive 2 somehow, i don't see how you get 19.

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Other answers:

5+2(5-(-2)) = +19
  • phi
what is \[2\int\limits_{-2}^{5}dx\]
YUP! come on and say int dude: "F that teacher!"
The teacher is right though?
If 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.
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Sorry, bad label in my graph, g(x) = 5/7, not 5x/7!
@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...
hartnn's description makes the most sense to me mathmatically. Thanks for the help!! :)
welcome ^_^

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