Graph Question

Feb 2017
36
0
henderson


Don't I just add what's under the graph?
 
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Country Boy

Math Team
Jan 2015
3,261
899
Alabama
You understand that the integral is the 'area under the curve' don't you? Here, since much of the graph is below the x-axis, that is really 'the area above the x-axis minus the area below the x-axis'.

Estimate those two areas by estimating what part of each square is in the region. Each square is 4 by 4 so has area 16. On the left, above the x-axis, I see, for x between -12 and 0 and y between 0 and 4, one full square, with a little more than half of the squares to the left and right of it. That would add to "two full squares" or 2(16)= 32. But the graph rises a little above that- I would estimate, for x between -12 and 0 and y larger than 4, about 1/2 of a full square so an additional 8. Do the same for the region on the right, below the x-axis, and subtract..

(You do understand that "estimate" means you aren't expected to give an exact answer, don't you?)
 
Feb 2017
36
0
henderson
You understand that the integral is the 'area under the curve' don't you? Here, since much of the graph is below the x-axis, that is really 'the area above the x-axis minus the area below the x-axis'.

Estimate those two areas by estimating what part of each square is in the region. Each square is 4 by 4 so has area 16. On the left, above the x-axis, I see, for x between -12 and 0 and y between 0 and 4, one full square, with a little more than half of the squares to the left and right of it. That would add to "two full squares" or 2(16)= 32. But the graph rises a little above that- I would estimate, for x between -12 and 0 and y larger than 4, about 1/2 of a full square so an additional 8. Do the same for the region on the right, below the x-axis, and subtract..

(You do understand that "estimate" means you aren't expected to give an exact answer, don't you?)
So I counted all the blocks and I get 22 above the line and 22 below the line,
which means 0, but the answer is wrong so I'm confused.
 
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