Explore BrainMass
Share

Find the exact area under the graph

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

** Please see the attached file for a Word formatted copy of the problem description **

1. let f(x) = x^2-2x+2 on the interval [-1, 2]. Sketch a graph of this function along with the rectangles that would be used to approximate the area under the curve using a right sum with n = 6. Be accurate and make your graph large.
a) Calculate the approximation in #1 stepwise, use appropriate notation.
b) Approximate the area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1, 2]. Using a right sum with n = 24. show all the relevant steps depending upon your approach as above.
c) Do the approximation in (a) and (b) overestimate or underestimate the true area? Explain without finding the actual area.

2. Find the exact area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1 , 2] using limits with a right sum. Correct notation is crucial.

3. Find the area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1 , 2] using a definite integral. Show all required work.

© BrainMass Inc. brainmass.com March 21, 2019, 10:23 pm ad1c9bdddf
https://brainmass.com/math/graphs-and-functions/finding-exact-area-under-graph-415021

Attachments

Solution Preview

I'm attaching the solution in .doc and .pdf formats.

** Please see the attached files for the complete solution response **

1. Calculating the area under the curve over the ...

Solution Summary

This solution carefully calculates the given approximation. The expert finds the exact area under a graph.

$2.19