Like this presentation? Why not share!

Area between curves

by djfromal on Oct 24, 2007

• 1,976 views

lesson from AP Calc

lesson from AP Calc

Views

Total Views
1,976
Views on SlideShare
1,971
Embed Views
5

Likes
0
16
0

1 Embed5

 http://www.slideshare.net 5

Categories

Uploaded via SlideShare as Microsoft PowerPoint

Area between curvesPresentation Transcript

• Area between Curves
• How do we define area “between” curves?
• Two non-intersecting functions with arbitrary boundaries
• Two functions that have 2 or more points of intersection
• “ Triangular” regions bounded by three functions
• Two non-intersecting functions with arbitrary boundaries
• Ex 1: Find the area bounded by f(x) = x 2 +2, g(x) = -x, x = 0, and x = 1
• Sketch the region(s)
• Draw representative rectangle
• Determine dx or dy
• Two functions that have 2 points of intersection
• Ex 2- Find the area bounded by
• f(x) = 2 – x 2 and g(x) = x
• Sketch the region
• Find the points of intersection
• f(x) = g(x) usually works
• Draw representative rectangle
• Determine dx or dy
• Two functions that have more than 2 points of intersection
• Ex 3- Find the area between the graphs of
• f(x) = 3x 3 -x 2 -10x and
• g(x) = -x 2 + 2x
• Sketch the region(s)
• Find the points of intersection
• f(x) = g(x) usually works
• Draw representative rectangle
• Determine dx or dy
• When do we ever use dy?
• Ex 4- Find the area bounded by
• x = 3 – y 2 and y = x - 1
• Sketch the region
• Find the points of intersection
• Solve a system of equations
• Draw representative rectangle
• Determine dx or dy
• “Triangular” regions bounded by three functions
• Ex 5- Find the area of the region bounded by: y = x, y = 2 – x,
• and y = -1
• Sketch the region
• Find the points of intersection
• Solve a system of equations
• Can this be done geometrically?
• Draw representative rectangle
• Determine dx or dy
• Can this be done in terms of the other variable?
• Quiz next session (45 min. maximum)
• Riemann Sums (left, right, midpoint, inscribed, circumscribed)
• Trapezoidal Rule
• Definite Integrals
• Fundamental Theorem of Calculus (I and II)
• Average Value of Function