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10 changes: 10 additions & 0 deletions
10
...pool/a4f79f7ArcLengthofaCurveandSurfaceArea1/a4f79f7ArcLengthofaCurveandSurfaceArea1.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,10 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1", | ||
| "title": "Calculating the Arc Length of a Function $$x$$", | ||
| "body": "", | ||
| "variabilization": {}, | ||
| "oer": "https://openstax.org/books/calculus-volume-1/pages/6-4-arc-length-of-a-curve-and-surface-area", | ||
| "license": 0.0, | ||
| "lesson": "6.4 KB", | ||
| "courseName": "Calculus Editor Sheet" | ||
| } |
12 changes: 12 additions & 0 deletions
12
...ps/a4f79f7ArcLengthofaCurveandSurfaceArea1a/a4f79f7ArcLengthofaCurveandSurfaceArea1a.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a", | ||
| "stepAnswer": [ | ||
| "$$2.268$$" | ||
| ], | ||
| "problemType": "TextBox", | ||
| "stepTitle": "Let \ud835\udc53(x) $$=$$ 2*x**{3/2}. Calculate the arc length of the graph of \ud835\udc53(x) over the interval [0,1]. Round the answer to three decimal places.", | ||
| "stepBody": "", | ||
| "answerType": "arithmetic", | ||
| "variabilization": {}, | ||
| "answerLatex": "$$2.268$$" | ||
| } |
60 changes: 60 additions & 0 deletions
60
...urveandSurfaceArea1a/tutoring/a4f79f7ArcLengthofaCurveandSurfaceArea1aDefaultPathway.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,60 @@ | ||
| [ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h1", | ||
| "type": "hint", | ||
| "dependencies": [], | ||
| "title": "Arc length formula", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + f'(x)**2), a, $$b$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h2", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h1" | ||
| ], | ||
| "title": "Take the derivative of f(x) and plug it into the integral with the given bounds", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + (3*x**{1/2})**2), $$0$$, $$1$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h3", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h2" | ||
| ], | ||
| "title": "Simplify $${f{\\left(x\\right)}}^2$$", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + 9*x), $$0$$, $$1$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h4", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h3" | ||
| ], | ||
| "title": "u substitution", | ||
| "text": "Perform u substitution with u $$=$$ $$1$$ + $$9x$$", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h5", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea1a-h4" | ||
| ], | ||
| "title": "Integral after u substitution", | ||
| "text": "Arc Length $$=$$ $$\\frac{1}{9}$$ * $$/int{sqrt(u)$$, $$1$$, $$10$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| } | ||
| ] |
10 changes: 10 additions & 0 deletions
10
...pool/a4f79f7ArcLengthofaCurveandSurfaceArea2/a4f79f7ArcLengthofaCurveandSurfaceArea2.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,10 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2", | ||
| "title": "Calculating the Arc Length of a Function $$x$$", | ||
| "body": "", | ||
| "variabilization": {}, | ||
| "oer": "https://openstax.org/books/calculus-volume-1/pages/6-4-arc-length-of-a-curve-and-surface-area", | ||
| "license": 0.0, | ||
| "lesson": "6.4 KB", | ||
| "courseName": "Calculus Editor Sheet" | ||
| } |
12 changes: 12 additions & 0 deletions
12
...ps/a4f79f7ArcLengthofaCurveandSurfaceArea2a/a4f79f7ArcLengthofaCurveandSurfaceArea2a.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2a", | ||
| "stepAnswer": [ | ||
| "$$1.657$$" | ||
| ], | ||
| "problemType": "TextBox", | ||
| "stepTitle": "Let \ud835\udc53(x) $$=$$ (4/3)*x**{3/2}. Calculate the arc length of the graph of \ud835\udc53(x) over the interval [0,1]. Round the answer to three decimal places.", | ||
| "stepBody": "", | ||
| "answerType": "arithmetic", | ||
| "variabilization": {}, | ||
| "answerLatex": "$$1.657$$" | ||
| } |
48 changes: 48 additions & 0 deletions
48
...urveandSurfaceArea2a/tutoring/a4f79f7ArcLengthofaCurveandSurfaceArea2aDefaultPathway.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,48 @@ | ||
| [ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h1", | ||
| "type": "hint", | ||
| "dependencies": [], | ||
| "title": "Arc length formula", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + f'(x)**2), a, $$b$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h2", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h1" | ||
| ], | ||
| "title": "Take the derivative of f(x)", | ||
| "text": "f'(x) $$=$$ $$\\frac{4}{3}$$ *(3/2) *x**{1/2} $$=$$ 2*x**{1/2}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h3", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h2" | ||
| ], | ||
| "title": "Plug the derivative into the integral with the given bounds", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + (2*x**{1/2})**2), $$0$$, $$1$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h4", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea2a-h3" | ||
| ], | ||
| "title": "Simplify $${f{\\left(x\\right)}}^2$$ and evaluate the integral", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + $$4x^2$$, $$0$$, $$1$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| } | ||
| ] |
10 changes: 10 additions & 0 deletions
10
...pool/a4f79f7ArcLengthofaCurveandSurfaceArea3/a4f79f7ArcLengthofaCurveandSurfaceArea3.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,10 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea3", | ||
| "title": "Using a Computer or Calculator to Determine the Arc Length of a Function of $$x$$. Round to three decimal places.", | ||
| "body": "", | ||
| "variabilization": {}, | ||
| "oer": "https://openstax.org/books/calculus-volume-1/pages/6-4-arc-length-of-a-curve-and-surface-area", | ||
| "license": 0.0, | ||
| "lesson": "6.4 KB", | ||
| "courseName": "Calculus Editor Sheet" | ||
| } |
12 changes: 12 additions & 0 deletions
12
...ps/a4f79f7ArcLengthofaCurveandSurfaceArea3a/a4f79f7ArcLengthofaCurveandSurfaceArea3a.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea3a", | ||
| "stepAnswer": [ | ||
| "$$8.269$$" | ||
| ], | ||
| "problemType": "TextBox", | ||
| "stepTitle": "Let \ud835\udc53(x) $$=$$ $$x^2$$ Calculate the arc length of the graph of \ud835\udc53(x) over the interval [1,3].", | ||
| "stepBody": "", | ||
| "answerType": "arithmetic", | ||
| "variabilization": {}, | ||
| "answerLatex": "$$8.269$$" | ||
| } |
36 changes: 36 additions & 0 deletions
36
...urveandSurfaceArea3a/tutoring/a4f79f7ArcLengthofaCurveandSurfaceArea3aDefaultPathway.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,36 @@ | ||
| [ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea3a-h1", | ||
| "type": "hint", | ||
| "dependencies": [], | ||
| "title": "Take the derivative of f(x) and plug it into the integral with the given bounds", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + (2*x)**2), $$1$$, $$3$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea3a-h2", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea3a-h1" | ||
| ], | ||
| "title": "Simplify $${f{\\left(x\\right)}}^2$$", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + 4*x**2), $$1$$, $$3$$, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea3a-h3", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea3a-h2" | ||
| ], | ||
| "title": "Use a computer, calculator, or another device to solve the integral.", | ||
| "text": "", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| } | ||
| ] |
10 changes: 10 additions & 0 deletions
10
...pool/a4f79f7ArcLengthofaCurveandSurfaceArea4/a4f79f7ArcLengthofaCurveandSurfaceArea4.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,10 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea4", | ||
| "title": "Using a Computer or Calculator to Determine the Arc Length of a Function of $$x$$. Round to three decimal places.", | ||
| "body": "", | ||
| "variabilization": {}, | ||
| "oer": "https://openstax.org/books/calculus-volume-1/pages/6-4-arc-length-of-a-curve-and-surface-area", | ||
| "license": 0.0, | ||
| "lesson": "6.4 KB", | ||
| "courseName": "Calculus Editor Sheet" | ||
| } |
12 changes: 12 additions & 0 deletions
12
...ps/a4f79f7ArcLengthofaCurveandSurfaceArea4a/a4f79f7ArcLengthofaCurveandSurfaceArea4a.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,12 @@ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea4a", | ||
| "stepAnswer": [ | ||
| "$$3.819$$" | ||
| ], | ||
| "problemType": "TextBox", | ||
| "stepTitle": "Let \ud835\udc53(x) $$=$$ sin(x) Calculate the arc length of the graph of \ud835\udc53(x) over the interval [0,/pi].", | ||
| "stepBody": "", | ||
| "answerType": "arithmetic", | ||
| "variabilization": {}, | ||
| "answerLatex": "$$3.819$$" | ||
| } |
36 changes: 36 additions & 0 deletions
36
...urveandSurfaceArea4a/tutoring/a4f79f7ArcLengthofaCurveandSurfaceArea4aDefaultPathway.json
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,36 @@ | ||
| [ | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea4a-h1", | ||
| "type": "hint", | ||
| "dependencies": [], | ||
| "title": "Take the derivative of f(x)", | ||
| "text": "f'(x) $$=$$ cos(x)", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea4a-h2", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea4a-h1" | ||
| ], | ||
| "title": "Plug the f'(x) into the arc length formula with the given bounds.", | ||
| "text": "Arc Length $$=$$ $$/int{sqrt(1$$ + (cos(x))**2), $$0$$, /pi, x}", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| }, | ||
| { | ||
| "id": "a4f79f7ArcLengthofaCurveandSurfaceArea4a-h3", | ||
| "type": "hint", | ||
| "dependencies": [ | ||
| "a4f79f7ArcLengthofaCurveandSurfaceArea4a-h2" | ||
| ], | ||
| "title": "Use a computer, calculator, or another device to solve the integral.", | ||
| "text": "", | ||
| "variabilization": {}, | ||
| "oer": "https://OATutor.io <OATutor>", | ||
| "license": "" | ||
| } | ||
| ] |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
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This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
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