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Introduction to Volumes by Slicing
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Classroom Contents
Applications of Calculus
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- 1 Introduction to Volumes by Slicing
- 2 Volumes by Slicing: Understanding the Annulus
- 3 Volumes by Slicing: Volume Generated by Rotation About y = 6
- 4 Volumes by Slicing: Rotation around x = 1
- 5 Calculating a Volume Rotated Around x = y (1 of 2: Determining Radius)
- 6 Calculating a Volume Rotated Around x = y (2 of 2: Forming/Evaluating Integral)
- 7 Applications & Implications of d/dx(½v²): General Case
- 8 Evaluating a Volume by Slices & by Shells
- 9 Introduction to Volumes by Cylindrical Shells: Visual Comparison with Slicing
- 10 Generalising from Volumes by Slices & Shells
- 11 Introduction to Volumes by Similar Cross-Section: Square Pyramid
- 12 Volumes by Cross-Section: Circular Slanted Roof
- 13 Useful Tricks for Evaluating Integrals from a Volume
- 14 Volume of a Sphere: Three Different Derivations
- 15 Volume of a Tetrahedron (by similar cross-sections)
- 16 Volumes by Cylindrical Shells (example question from exam)
- 17 Volumes by Slices (example question from exam: hole drilled through sphere)
- 18 Newton's Method (1 of 2: How does it work?)
- 19 Newton's Method (2 of 2: Potential Dangers)
- 20 Volumes (Ext II) (How does Volumes Fit in with the other mathematics courses)
- 21 Volumes by Slicing (1 of 4: Proving the Volume formula integral)
- 22 Volumes by Slicing (2 of 4: Finding the Volume of a Typical Slice to calculate a volume)
- 23 Volumes by Slicing (3 of 4: Rotating an area around an axis apart from coordinate axis)
- 24 Volumes by Slicing (4 of 4: Harder Volumes by Slicing Question)
- 25 Harder Volumes by Slicing (1 of 3: Finding the orientation of slices and volume of typical slice)
- 26 Harder Volumes by Slicing (2 of 3: Using a triangle to find x in terms of a defined variable 'h')
- 27 Harder Volumes by Slicing (3 of 3: Converting to one single variable to integrate for the volume)
- 28 Volume by Cylindrical Shells (3 of 3: Finding the Volume via Cylindrical Shells and which to choose)
- 29 Volumes by Shells (1 of 3: Overview of Volumes done so far)
- 30 Volumes by Shells (2 of 3: Introduction to Cylindrical Shells & finding typical volume)
- 31 Worked Example of Volumes by shells (Finding the volume of an area between two curves)
- 32 Choosing between Slices and Shells (1 of 2: Volume when cosx is rotated around y axis by slicing)
- 33 Choosing between Slices and Shells (2 of 2: Finding the volume and the benefits of shell method)
- 34 Volumes by Similar Cross Sections (1 of 2: Using integration to find a non-rotated volume)
- 35 Volumes by Similar Cross Sections (2 of 2: Using a typical cross section volume to find the volume)
- 36 Volumes by Similar Cross Section (1 of 4: Presenting information from the question with a diagram)
- 37 Volumes by Similar Cross Section (2 of 4: Finding the area of a typical volume)
- 38 Volumes by Cross Section (4 of 4: Finding the side length in term of h and finding the volume)
- 39 Volumes by Similar Cross Section (3 of 4: Finding the volume of a double quarter pipe)
- 40 Simpson's Rule for Volumes
