Using Reimann Sums
Not what you're looking for?
Use the 'midpoint' rule for calculating the integral of x^3 on the domain [6,7] using n=2,5, and 10 equally wide rectangles. Then calculate the integral on the domain [2,4].
Purchase this Solution
Solution Summary
The following shows a direct calculation of the integral of a function using a few numbers of Riemann Sum rectangles as well as an infinite number of Riemann Sum rectangles. It is also apparent how this formulation is related to the integral.
Solution Preview
The following is an explanation of the three typical ways of thinking about using Riemann sums to approximate an integral, left-point, midpoint, and right-point approximations. The total area will become the summation of an increasing number of rectangles in the domain whose widht will decrease proportinately. For a few rectangles, the total area will be a simple sum of a few products - the products being the individual rectangles height times width. For many rectangles one should use Faulhaber's formula and limits, and the correct answer will follow.
restart
with (Student [Calculus1]) :
f := x ---> x^3 (1)
Essentially, integration against one variable (as in dx for this case) can be thought of as determining the
area under the curve (bounded by the y=0 line). So what one can do is replace the area with rectangles,
which in this case are equal width for the 'n' rectangles chosen (here there are 2, 5, and then 10, as in the
first three parts of your ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
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.
Probability Quiz
Some questions on probability