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

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 ?

- anonymous

i just did the same, but i didn't get 19...

- anonymous

@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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## More answers

- hartnn

5+2(5-(-2)) = +19

- phi

what is
\[2\int\limits_{-2}^{5}dx\]

- anonymous

YUP! come on and say int dude: "F that teacher!"

- anonymous

it*

- anonymous

6

- anonymous

The teacher is right though?

- whpalmer4

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.

##### 1 Attachment

- whpalmer4

Sorry, bad label in my graph, g(x) = 5/7, not 5x/7!

- ZeHanz

@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

hartnn's description makes the most sense to me mathmatically. Thanks for the help!! :)

- hartnn

welcome ^_^

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