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Loser66
 one year ago
\[\int_{3}^{3} x+1dx\]
Please, help
Loser66
 one year ago
\[\int_{3}^{3} x+1dx\] Please, help

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Integrate separately on parts of the domain that are convenient is the quick tip. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Or, just draw it and find the area. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Will do, I'll do the drawing method since it's more clever.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I show you my confusion.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433638297626:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0no confuse, hehehe.. I am sorry. I posted the wrong question. But I would like to know how to solve it traditionally

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0No 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.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I meant integrate separately..........

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0First, 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.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0It may take a bit of pondering to fully see that. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Then, this naturally gives us two convenient domains. (infinity, 1) and (1, +infinity). The split point is at x = 1.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0We want (3, 3) so we break this into the domains (3, 1), and (1, 3).

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0Then we integrate using the definition of absolute value.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{3}^3 x + 1 \ dx = \int\limits_{3}^{1} (x+1) \ dx + \int\limits_{1}^3 x+1 \ dx\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.0The integration can then be carried out as usual.
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