Area Between Curves.pdf - 14.2 \u2013 Area Between Curves We now know that we can calculate the Definite Integral for any continuous function on a closed

Area Between Curves.pdf - 14.2 u2013 Area Between Curves...

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14.2 Area Between Curves We now know that we can calculate the Definite Integral for any continuous function, ?(𝑥) , on a closed interval [?, ?] , by using the Fundamental Theorem of Calculus: ∫ 𝒇(𝒙)𝒅𝒙 = 𝑭(?) − 𝑭(?) ? ? where 𝐹 (𝑥) = ?(𝑥). 14.2 Area Between Curves When given two continuous functions (graphical referred to as curves) over the same interval, we can now find the area between these two curves. In this case, we always want to make sure that the total area between these curves on the given interval is calculated as the positive result representing the actual total area. To do this, we need to first determine which of the functions is above the other function over the entire interval. We will call this the TOP function and the other one will be the BOTTOM function. Then the area between these curves over the interval [?, ?] can be found by calculating the Definite Integral ∫ (𝑇?? − 𝐵?𝑇𝑇?𝑀)𝑑𝑥 ? ? NOTE: It will always be in your best interest to algebraically simplify within the integral before completing the integration step.

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