Section 6.1: More About Areas

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Presentation transcript:

Section 6.1: More About Areas Practice HW from Stewart Textbook (not to hand in) p. 446 # 1-15 odd

Areas Between Curves Suppose we are given a continuous function y = f (x) where over the interval [a, b]. Recall:

Suppose we are given two functions f and g and we want to find the area bounded between the functions from x = a and x = b.

Area Between Two Curves Given f and g are continuous functions on [a, b] and for all x in [a, b]. Then

Example 1: Determine the area bounded between the graphs of and between x = -1 and x = 2. Solution:

Note: When asked to find the area bound by two graphs, to find the interval we many times have to find the points of intersection.

Example 2: Sketch the graph and find the area enclosed by the graphs of and . Solution:

Note: The upper and lower curves can switch over an interval. In this case, we must divide the interval and switch the upper and lower curves when integrating to find the area.

Example 3: Sketch the graph and find the area enclosed by the graphs of , , and where x > 0. Solution: (In typewritten notes)

Horizontal Area Representation Involves integrating with respect to y to find the area when x is written as a function of y.

Example 4: Find the area enclosed by and . Solution: