Definite Integrals: Negative Area EXPLAINED with Examples

Learn what it means when a Definite Integral returns a negative answer. This does not mean that you broke Math by finding a negative area. Definite Integrals find the area between a function and the x-axis. However, they count area above the x-axis as positive area and area below the x-axis as negative area. In calculating the final result, the negative area will cancel out some or all of the positive area to return a negative, zero or positive answer. This video explains the topic and goes through an example problem to illustrate the concept. Skills with integrals, antiderivatives and derivatives are necessary for this video.
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[@angelisvegan5826]

Great explanation

[@Vladyslav_Rehan]

Thanks!

[@AceTutors1]

You are very welcome!

[@Sharmilananawarenanawre8871]

very well explained

[@AceTutors1]

Much appreciated Yogesh!

[@pranjalarora3193]

​@@AceTutors1I have a doub that what calculations makes the area below curve negative

[@quietguy9484]

I understand the concept, but it still feels strange to me. That last example in particular seemed to go against my intuition because there is clearly an area there. To say that the area is zero feels unacceptable to me because I can clearly see that there is space inbetween the curve and x-axis.

[@shahedhossainimran1]

I think it's just the sum of the area that is zero. if you are asked for the total area without caring about signs, then ( I think) you just add both of them up.

[@lMaxe69]

Not good, you did not show how to solve it and only showed the wrong answer