## Bladerunner1122 2 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.

1. 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 ?

2. IStutts

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

3. IStutts

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

4. hartnn

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

5. phi

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

6. IStutts

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

7. IStutts

it*

8. IStutts

6

The teacher is right though?

10. 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.

11. whpalmer4

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

12. 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...

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

14. hartnn

welcome ^_^