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Category 1: Area Under the Curve Part II 1. What is the area under the curve in

ID: 2843348 • Letter: C

Question

Category 1: Area Under the Curve Part II




1. What is the area under the curve in the interval [-3, 3] for the function f(x)=x^3-9x^2? What happens when you find the value of the definite integral ?_(-3)^3?x^3-9x^2 dx?? Why can

What is the area under the curve in the interval [-3, 3] for the function f(x)=x^3-9x^2? What happens when you find the value of the definite integral ?_(-3)^3?x^3-9x^2 dx?? Why can't this be the area under the curve above? How would you go about determining the area under the curve so that you avoid the cancelling out nature of the area above the x-axis with the area below the x-axis?

Explanation / Answer

The value of function f(x) is psitive for x>0 and negative for x<0

so if you intergrate ??x^3-9x^2 dx?from -3 to +3, the negative integral value from (-3,0) will cancel out the positive integral value from (0,3) and resulting value will be 0
if we have to find the area of the f(x) in term of magnitude then we have to calculate the below integrals

?_(-3)^0?|x^3-9x^2| dx?+ ?_(0)^3?|x^3-9x^2| dx?

so Area under the curve is 121.5 unit^2

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