× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
Home Q & A Board Science-Related Homework Help Mathematics
New Topic  
calcourse calcourse
wrote...
Posts: 19
Rep: 0 0
11 years ago
A left sum and a right sum are used to estimate the area between the graph of the function f(x) = sinx and the x-axis from x = 0 to x = 1.5. Which of the two sums gives an underestimate of the value of the area? Justify your answer

Use a left sum with 4 rectangles of equal width to estimate the area between the graph of f(x) = 2x2 and the x-axis, between x = 0 and x = 8.

Use the summation formulas to find the exact area between the graph of f(x) = x2 + 4 and the x-axis from x = 0 to x = 2.
Read 1290 times
2 Replies

Related Topics

Replies
wrote...
#1
11 years ago
Quote from: calcourse (11 years ago)
A left sum and a right sum are used to estimate the area between the graph of the function f(x) = sinx and the x-axis from x = 0 to x = 1.5. Which of the two sums gives an underestimate of the value of the area? Justify your answer

This is basically the area of the curve between 0 and pi/2. In this case, since the graph is increasing in this interval, the left sum takes the rectangles and inscribes them. By doing this, the top left of each rectangle touches the sine graph while the right side ends up inside/underneath creating little gaps or area that do not get counted.
wrote...
#2
11 years ago
Quote from: etaylor6 (11 years ago)
Quote from: calcourse (11 years ago)
A left sum and a right sum are used to estimate the area between the graph of the function f(x) = sinx and the x-axis from x = 0 to x = 1.5. Which of the two sums gives an underestimate of the value of the area? Justify your answer

This is basically the area of the curve between 0 and pi/2. In this case, since the graph is increasing in this interval, the left sum takes the rectangles and inscribes them. By doing this, the top left of each rectangle touches the sine graph while the right side ends up inside/underneath creating little gaps or area that do not get counted.


Ah, etaylor6 got to this question first. But yeah, everything he said was right!
New Topic      
Quick Reply
Explore
Post your homework questions and get free online help from our incredible volunteers
  1277 People Browsing
Start New Topic Take the Tour CoursesNew Study Tools Topics Trending Browse by Textbook
Related Images
  
 81
  
 169
  
 894