Calculus

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!

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  1. The links are not working. I’m going to post new ones under this post.

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  2. 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

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  3. There are several good Riemann Sum calculators online to verify your answers.

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    oobleck
  4. 1. 3.196
    2. 0.9243
    3. 88.8

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