Let f(x) = Vsin x. Compute the midpoint sum for f corresponding to the partition of [0, 2] into 20 intervals of equal length.

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I want an answer of question number 2.

Let f(x) = Vsin x. Compute the midpoint sum for f
corresponding to the partition of [0, 2] into 20 intervals
of equal length.
Transcribed Image Text:Let f(x) = Vsin x. Compute the midpoint sum for f corresponding to the partition of [0, 2] into 20 intervals of equal length.
Expert Solution
Step 1

Draw the graph of the function Calculus homework question answer, step 1, image 1.

Calculus homework question answer, step 1, image 2

Step 2

To find the midpoint sum of f corresponding to the interval [0,2],  subdivide the area under the graph in the interval [0,2] into 20 rectangles of equal width that is 0.1 . 

Calculus homework question answer, step 2, image 1

Step 3

Set Calculus homework question answer, step 3, image 1.

Mid-point of line between interval [0,0.1] =Calculus homework question answer, step 3, image 2

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 3, image 3

Area under the interval [0,0.1] =Calculus homework question answer, step 3, image 4

Mid-point of line between interval [0.1,0.2] =Calculus homework question answer, step 3, image 5

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 3, image 6

Area under the interval [0.1,0.2] =

Calculus homework question answer, step 3, image 7

Step 4

Mid-point of line between interval [0.2,0.3] =Calculus homework question answer, step 4, image 1

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 4, image 2

Area under the interval [0.2,0.3] =Calculus homework question answer, step 4, image 3

Mid-point of line between interval [0.3,0.4] =Calculus homework question answer, step 4, image 4

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 4, image 5

Area under the interval [0.3,0.4] =Calculus homework question answer, step 4, image 6

Step 5

Mid-point of line between interval [0.4,0.5] =Calculus homework question answer, step 5, image 1

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 5, image 2

Area under the interval [0.4,0.5] =Calculus homework question answer, step 5, image 3

Mid-point of line between interval [0.5,0.6] =Calculus homework question answer, step 5, image 4

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 5, image 5

Area under the interval [0.5,0.6] =Calculus homework question answer, step 5, image 6

Mid-point of line between interval [0.6,0.7]=Calculus homework question answer, step 5, image 7

Substitute the value of mid-point in the function f(x) and find the value of y.

Calculus homework question answer, step 5, image 8

Area under the interval [0.6,0.7] =Calculus homework question answer, step 5, image 9

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