Question
Use midpoints to approximate the area under the curve (see link) on the interval [0,1] using 10 equal subdivisions.
imagizer.imageshack.us/v2/800x600q90/707/5b9m.jpg
3.157---my answer (but I don't understand midpoints)
3.196
3.407
2.078
2.780
2. Use right-hand endpoints and 6 equal subdivisions to approximate the area beneath the curve on the interval [0, 6].
imagizer.imageshack.us/v2/800x600q90/38/7ruq.jpg
0.9243
1.405
1.897
1.021--my answer (but got several different answers close to 1)
1.682
3. The table below gives data points for the continuous function y = f(x)
imagizer.imageshack.us/v2/800x600q90/706/khd9.jpg
Approximate the area under the curve y = f(x) on the interval [0, 2] using left-hand endpoints and 10 equal subdivisions. You get Area ≈
96.8
454----my answer
88.8
90.8
444
4. Consider the curve and the region under f (x) between x = 1 and x = 3, which is graphed below.
imagizer.imageshack.us/v2/800x600q90/23/f1o5.jpg
Suppose L is the left-hand endpoint Riemann sum with 15 subdivisions, R is the right-hand endpoint Riemann sum with 15 subdivisions, and A is the true area of this region. Which of the following is correct?
R < L < A
L < A < R----my answer
L = A = R
R < A < L
A < R < L
5. The function y = f(x) is graphed below:
imagizer.imageshack.us/v2/800x600q90/841/a45g.jpg
Which of the following Riemann sums yields the exact area under the curve on the interval [0, 6]?
I. R=E(above=4)below=k=1 f(wk)deltaxk, where subdivisions are at {0, 2, 3, 4, 6} and right-hand endpoints are used.
II. R=E(above=4)below=k=1 f(wk)deltaxk, where subdivisions are at {0, 2, 3, 4, 6} and midpoints are used.
III.R=E(above=6)below=k=1 f(wk)deltaxk , where 6 equal subdivisions and right-hand endpoints are used.
I only
II only
III only
I and II only---my answer
I, II, and III
6. Here is a graph of the function:
imagizer.imageshack.us/v2/800x600q90/826/zebj.jpg
Estimate the total area under this curve on the interval [0, 12] with a Riemann sum using 36 equal subdivisions and circumscribed rectangles. Hint: use symmetry to make this problem easier.
57.340
86.634-- my answer
14.439
49.914
28.044
I need help with these for a practice test, thank you in advance! Please let me know if my answers are right or what the correct answer is if they are wrong! Thank you!
imagizer.imageshack.us/v2/800x600q90/707/5b9m.jpg
3.157---my answer (but I don't understand midpoints)
3.196
3.407
2.078
2.780
2. Use right-hand endpoints and 6 equal subdivisions to approximate the area beneath the curve on the interval [0, 6].
imagizer.imageshack.us/v2/800x600q90/38/7ruq.jpg
0.9243
1.405
1.897
1.021--my answer (but got several different answers close to 1)
1.682
3. The table below gives data points for the continuous function y = f(x)
imagizer.imageshack.us/v2/800x600q90/706/khd9.jpg
Approximate the area under the curve y = f(x) on the interval [0, 2] using left-hand endpoints and 10 equal subdivisions. You get Area ≈
96.8
454----my answer
88.8
90.8
444
4. Consider the curve and the region under f (x) between x = 1 and x = 3, which is graphed below.
imagizer.imageshack.us/v2/800x600q90/23/f1o5.jpg
Suppose L is the left-hand endpoint Riemann sum with 15 subdivisions, R is the right-hand endpoint Riemann sum with 15 subdivisions, and A is the true area of this region. Which of the following is correct?
R < L < A
L < A < R----my answer
L = A = R
R < A < L
A < R < L
5. The function y = f(x) is graphed below:
imagizer.imageshack.us/v2/800x600q90/841/a45g.jpg
Which of the following Riemann sums yields the exact area under the curve on the interval [0, 6]?
I. R=E(above=4)below=k=1 f(wk)deltaxk, where subdivisions are at {0, 2, 3, 4, 6} and right-hand endpoints are used.
II. R=E(above=4)below=k=1 f(wk)deltaxk, where subdivisions are at {0, 2, 3, 4, 6} and midpoints are used.
III.R=E(above=6)below=k=1 f(wk)deltaxk , where 6 equal subdivisions and right-hand endpoints are used.
I only
II only
III only
I and II only---my answer
I, II, and III
6. Here is a graph of the function:
imagizer.imageshack.us/v2/800x600q90/826/zebj.jpg
Estimate the total area under this curve on the interval [0, 12] with a Riemann sum using 36 equal subdivisions and circumscribed rectangles. Hint: use symmetry to make this problem easier.
57.340
86.634-- my answer
14.439
49.914
28.044
I need help with these for a practice test, thank you in advance! Please let me know if my answers are right or what the correct answer is if they are wrong! Thank you!
Answers
Erik
The links are not working. I’m going to post new ones under this post.
Erik
Question 1: ibb.co/9TYhZV7
Question 2: ibb.co/2Y6chSQ
Question 3: ibb.co/Gkgq87n
Question 4: ibb.co/4Zf4rvg
Question 5: ibb.co/4SjW7xY
Question 6: ibb.co/LpLST3C
Question 2: ibb.co/2Y6chSQ
Question 3: ibb.co/Gkgq87n
Question 4: ibb.co/4Zf4rvg
Question 5: ibb.co/4SjW7xY
Question 6: ibb.co/LpLST3C
oobleck
There are several good Riemann Sum calculators online to verify your answers.
Ellie
1. 3.196
2. 0.9243
3. 88.8
2. 0.9243
3. 88.8
red
4. R < A < L