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.

Question

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.

hartnn · Answer

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 · Answer

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

anonymous · Answer

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

hartnn · Answer

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

phi · Answer

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

anonymous · Answer

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

anonymous · Answer

it*

anonymous · Answer

6

anonymous · Answer

The teacher is right though?

whpalmer4 · Answer

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.

whpalmer4 · Answer

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

zehanz · Answer

@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 · Answer

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

hartnn · Answer

welcome ^_^