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3.5 Integration as the Summation of Areas

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3.5 Integration as the Summation of Areas

(A) Area of the region between a Curve and the x-axis.



Area of the shaded region;  A = ∫ a b y d x


(B) Area of the region between a curve and the y-axis.


Area of the shaded region;  A = ∫ a b x d y


(C) Area of the region between a curve and a straight line.


Area of the shaded region;  A = ∫ a b f ( x ) d x − ∫ a b g ( x ) d x