to find the area under the curve warm-up: graph. area under a curve for [0, 3] the area between the...
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To find the area under the curve
Warm-Up:Graph xxf 2
Area under a curve for [0, 3] The area between the x-axis and the function
Warm-up
What is the area under the function on the interval [0, 3]?
Find the area of the function from [0, 5]
Find the area under the function
Problem???
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
middle
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
middle
right
Riemann Sums Sum the areas of all rectangle
-the height of each rectangle is f(x)-the width of each rectangle is dx
Use Riemann sums to find the area under the curve
xf
Left Riemann Sums Let dx = 0.5
Left Riemann Sum
Middle Riemann Sum
Middle Riemann Sum
Right Riemann Sums
Right Riemann Sums
Right vs Left Riemann Sums
Determine the following Given a function, an interval and dx
Find:1. Sketch the function and the approximating rectangles using the midpoints2. Approximate the area under the curve
On the interval [0, 4] 216 xxf dx = 1
1. Sketch
2. Area
216 xxf
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