Loser66 one year ago $\int_{-3}^{3} |x+1|dx$ Please, help

1. jtvatsim

Integrate separately on parts of the domain that are convenient is the quick tip. :)

2. Loser66

3. jtvatsim

Or, just draw it and find the area. :)

4. jtvatsim

Will do, I'll do the drawing method since it's more clever.

5. Loser66

I show you my confusion.

6. jtvatsim

|dw:1433638297626:dw|

7. Loser66

no confuse, hehehe.. I am sorry. I posted the wrong question. But I would like to know how to solve it traditionally

8. jtvatsim

No worries. :) You should be able to see from the graph that the answer is the area of two triangles. But I will do the traditional (algebraic nastiness) approach as well.

9. Loser66

I meant integrate separately..........

10. jtvatsim

First, we need the definition of what |x + 1| means: |x + 1| = { x + 1, for x >= -1; -(x + 1), for x < -1. This is the usual, "make the number positive" rule we remember in our heads expressed algebraically.

11. jtvatsim

It may take a bit of pondering to fully see that. :)

12. jtvatsim

Then, this naturally gives us two convenient domains. (-infinity, -1) and (-1, +infinity). The split point is at x = -1.

13. jtvatsim

We want (-3, 3) so we break this into the domains (-3, -1), and (-1, 3).

14. jtvatsim

Then we integrate using the definition of absolute value.

15. jtvatsim

$\int\limits_{-3}^3 |x + 1| \ dx = \int\limits_{-3}^{-1} -(x+1) \ dx + \int\limits_{-1}^3 x+1 \ dx$

16. jtvatsim

The integration can then be carried out as usual.

17. Loser66

Got you. Thanks a lot

18. jtvatsim

No problems! :)

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