Limits : Evaluating Integrals, Anti-Differentiation and Area Between Curves
Not what you're looking for?
(a) Consider the attached limit of summed terms
(i) Explain why each of the sums in the attached expression gives an over-estimate of the area beneath the curve {see attachment}
(ii) Evaluate this limiting sum, using the expression {see attachment}
(iii) Check your answer in (ii), by using the fundamental theorem of calculus to evaluate the corresponding definite integral usuing anti-differentiation
(b) Without evaluating the integral, find F'(x) where {see attachment}
(c) Write down, and evaluate, an integral expression for the area of the region enclosed by the two curves {see attachment} for values of x between x = 1 and x = 3. Sketch the region, and check your answer matches an approximation to the area based in your sketch.
Purchase this Solution
Solution Summary
Integrals, limiting sums and area between curves are investigated. The solution is well explained.
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
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.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.