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Numerade Educator

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Problem 40 Medium Difficulty

Evaluate the integral by interpreting it in terms of areas.

$ \displaystyle \int^1_0 \bigl| 2x - 1 \bigr| \, dx $

Answer

0.5

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Video Transcript

to evaluate the integral given here the absolute value of two X minus one. We could just go ahead and draft that. And then we want to find the area between zero and one half and zero on one half and one. So this point right here, 0.5. And because of that, we have Well, we have a height on the left side. If we were to plug zero into this, we'd get one. So it's got a height of one on this side. We plug one into this. We also get one. We got two triangles that have a height of one and bases of 0.5. And so we're basically just adding thes two together here. Uh huh. But that's 11 half of one time 0.5 is actually 0.25 That's its area and the one over to the right there. So plus, Plus, that one has the identical area of 0.25 because it's half of half times one. So therefore both of these added together we'll end up giving us a total area for the evaluation of the integral ends up being 0.5 positive since everything's above the X axis