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Bladerunner1122

  • 3 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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  1. hartnn
    • 3 years ago
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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 ?

  2. IStutts
    • 3 years ago
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    i just did the same, but i didn't get 19...

  3. IStutts
    • 3 years ago
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    @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
    • 3 years ago
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    5+2(5-(-2)) = +19

  5. phi
    • 3 years ago
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    what is \[2\int\limits_{-2}^{5}dx\]

  6. IStutts
    • 3 years ago
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    YUP! come on and say int dude: "F that teacher!"

  7. IStutts
    • 3 years ago
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    it*

  8. IStutts
    • 3 years ago
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    6

  9. Bladerunner1122
    • 3 years ago
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    The teacher is right though?

  10. whpalmer4
    • 3 years ago
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    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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  11. whpalmer4
    • 3 years ago
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    Sorry, bad label in my graph, g(x) = 5/7, not 5x/7!

  12. ZeHanz
    • 3 years ago
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    @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...

  13. Bladerunner1122
    • 3 years ago
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    hartnn's description makes the most sense to me mathmatically. Thanks for the help!! :)

  14. hartnn
    • 3 years ago
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    welcome ^_^

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