# finding area using integrationWatch

#1
so I know that if we integrate between two x-coordiates you will get an area. if that area is below the x-axis, the area will appear as a negative value. Would that happen to parametric and polar integration as well? If i integrate an area below x-axis using parametric and polar coordinates, would it appear as positive value?
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11 months ago
#2
(Original post by Iconic_panda)
so I know that if we integrate between two x-coordiates you will get an area. if that area is below the x-axis, the area will appear as a negative value. Would that happen to parametric and polar integration as well? If i integrate an area below x-axis using parametric and polar coordinates, would it appear as positive value?
All of those can be answered in one go if you consider what an integral actually is for an area. For you are essentially summing up the products from to . If we get that . The only way the product can be -ve is if in the domain, hence how we get -ve area.

Same principle applies to any other integral. For polar, we have and if then it cannot be negative. Generally, we have so is +ve, and the product is +ve and so the area is always +ve. You can get it being -ve if the larger limit is the lower limit so that is -ve, or is
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