Area under a curve
Not what you're looking for?
• Find an estimate of the area under the graph of between and above the -axis. Use four left endpoint rectangles.
• Find an estimate of the area under the graph of between and above the -axis. Use four right endpoint rectangles.
• Find an estimate of the area under the graph of between and . Use four left endpoint rectangles.
• Find an estimate of the area under the graph of between and . Use two midpoint rectangles.
Purchase this Solution
Solution Summary
Area under the curve for a given range is calculated in different ways.
Solution Preview
Please see the attached file.
• Find an estimate of the area under the graph of between and above the -axis. Use four left endpoint rectangles.
The curve y = x2 is shown in diagram. At x = 0; y = 02 = 0, hence the curve is passing through the origin (0, 0) and at x = 2; y = 22 = 4 hence the curve is passing through the point (2, 4).
As to estimate the area under the curve from x = 0 to x = 2 we have to use four rectangles, the width of each rectangle should be (2 - 0)/4 = ½ = 0.5.
Now as we have to take left endpoint rectangles and the left points of the rectangles will have x coordinates
x = 0, 0.5, 1.0 and 1.5 respectively and their heights will be
y = 0, 0.25, 1.0 and 2.25.
The height of the first rectangle is zero and hence its area is 0.5*0 = 0
The height of the second rectangle is 0.25 and hence its area is 0.5*0.25 = 0.125
The height of the third rectangle is 1 and hence its area is 0.5*1 = 0.5 and
The height of the fourth rectangle is 2.25 and ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Probability Quiz
Some questions on probability