AP Calculus Ms. Battaglia

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Presentation transcript:

AP Calculus Ms. Battaglia 7-1 Area of a Region Between Two Curves 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

Finding the Area of a Region Between Two Curves Find the area of the region bounded by the graphs of y = x2 + 2, y = -x, x = 0 and x = 1.

A Region Lying Between Two Intersecting Graphs Find the area of the region bounded by the graphs of f(x) = 2 – x2 and g(x) = x.

A Region Lying Between Two Intersecting Graphs The sine and cosine curves intersect infinitely many times, bounding regions of equal areas. Find the area of one of these regions.

Curves That Intersect at More Than Two Points Find the area of the region between the graphs of f(x)=3x3-x2-10x and g(x)=-x2+2x

Horizontal Representative Rectangles Find the area of the region bounded by the graphs of x=3-y2 and x=y+1

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

Describing Integration as an Accumulation Process Find the area of the region bounded by the graph of y=4-x2 and the x-axis. Describe the integration as an accumulation process.

Classwork/Homework Read 7.1 Page 454 #3,4,19,20,21, using calculator 24,25,30