7 1 Area of a Region Between Two

7 -1 Area of a Region Between Two Curves (Day 2) Objective: Find the area of a region between two curves and intersecting curves using integration. AP Calculus Ms. Battaglia

Area of a Region Between Two Curves If f and g are continuous on [a, b] and g(x)<f(x) for all x in [a, b], then the area of the region bounded by the graphs of f and g and the vertical lines x=a and x=b is

Example Set up the definite integral that gives the area of the region. y = x 2 -6 x and y = 0

Example Set up the definite integral that gives the area of the region. y = x 2+2 x+1 and y = 2 x+5

Example Sketch the region bounded by the graphs of the algebraic functions and find the area of the region.

Integration as an Accumulation Process Known precalculus Formula Representative element New integration formula For example, the area formula in this section was developed as follows: A=(height)(width) ΔA=[f(x)-g(x)]Δx

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