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# Negative definite integrals

We learned that definite integrals give us the area under the curve and above the x-axis. But what if the curve itself is below the x-axis? In this case, the definite integral is still related to area, but it's negative. See how this works and get some intuition for why this is so.

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• what happen when a is greater than b?
• The function will become negative because you are going in the reverse order.
• How the unit of the area is the only meter?
shouldn't it be Meter squared? at 3.40
(1 vote)
• We're multiplying velocity, measured in meters per second (m/s), and time, measured in seconds (s), so the resulting unit will be
(m/s) ∙ s = m ∙ s/s = m ∙ 1 = m (meters).
• This question has always bugged me: which is greater: -8m/s or 4m/s? Or does it not make sense to ask this question at all?
(1 vote)
• I think the difference between speed and velocity are key here.

Speed is pure numbers. There can be no negative speed. if a car is moving to the right at 4 m/s and another os moving left at 8 m/s, the left one may be moving in the negative direction, but speed doesn't account for that.

Velocity DOES take into account direction. That being said, it can have parts that are negative and parts that are positive. for instance if you had a space ship moving tot he right and down, right is the positive x directiona dn down is the negative y direction So it is very hard to compare things like that. It all depends on the question you are asking
• what if a=-6; b=-2; integral(f(x)=6), what would be the area?+24 or -24?
(1 vote)
• If you're integrating from -6 to -2, you're taking the positive area because -6 is less than -2. f(x) = 6 is always above the x-axis, so this means that your area will be positive, as you're taking the integral in the normal direction of a function that has a positive area.