Area Between Two Curves
43 min 4 Examples
- Overview of finding area between two curves
- Finding area between curves given the limits of integration and when limits must be determined (Example #1 and #2)
- Dividing the region and using the y-axis to find area between curves (Example #3 and #4)
- Introduction to how area between curves relates to finding volume
Volumes with Known Cross Sections
38 min 4 Examples
- Overview of how we find volume using area of a base and a cross-sectional slice
- All Formulas needed for finding volume using Cross Sections
- 4 Examples where we find volume using all of our cross sectional formulas, for areas that are both perpendicular to the x-axis and also the y-axis
Disk Method
1 hr 52 min 10 Examples
- Solids of Revolution using the Disk Method
- Find the volume by revolving bounded region about x-axis (Example #1)
- Determine the volume formed by revolving bounded region about x-axis (Examples #2-3)
- Calculate the volume formed by revolving bounded region about y-axis (Examples #4-5)
- Find the volume by revolving bounded region about y=k (Examples #6-7)
- Find the volume by revolving bounded region about x=h (Examples #8-9)
- Use two integral statements to find the volume by revolving about x-axis (Example #10)
Washer Method
2 hr 26 min 7 Examples
- Solids of Revolution – Washer Method Formulas
- Find the volume of the solid about the axes (Example #1a-b)
- Use the washer method to find the volume about the axes (Example #2a-b)
- Find the volume of the solid formed by revolving about the y-axis (Example #3)
- Use the washer method to find the volume about y=k (Example #4a-b)
- Use the washer method to find the volume about x=h (Example #4c-d)
- Calculate the volume of the solid about the x-axis (Example #5a)
- Calculate the volume of the solid about the line x=-1 (Example #5b)
- Set up the integral to find the volume of the solid about axis of revolution (Example #5c-e)
- Find the volume if a circle is revolved about horizontal line (Example #6)
- Use the disk and washer method to find the volume (Example #7)
Solids of Revolution – Shell Method
1 hr 38 min 9 Examples
- Cylindrical Shell Method Overview and Formulas
- Comparing disk and shell method (Example #1 and #2)
- Using shell method to find volume of solids about vertical and horizontal axes (Examples #3-6)
- Finding volume using cylindrical shell method and volume of y=sinx about y-axis (Examples #7-9)
Arc Length Formula Calculus
1 hr 26 min 7 Examples
- Arc Length Formula for Calculus
- Set-up the integral to find the length of the smooth curve (Example #1a-c)
- Calculate the length of the curve (Examples #2-3)
- Find the arc length over the given interval (Example #4)
- Overview of Surface Area of Revolution Formulas
- Find the resulting surface area generated by revolving about the x-axis (Example #5)
- Find the surface area about the x-axis (Example #6)
- Calculate the surface area about the y-axis (Example #7)
Work and Hooke’s Law
59 min 7 Examples
- Overview of Work and Hooke’s Law
- Finding work done in stretching a spring beyond its natural length (Hooke’s Law Example #1 and #2)
- Finding the force needed in stretching a spring beyond its natural length (Hooke’s Law Example #3)
- Review of Work, Force, and Units
- Finding work needed to lift a bucket and rope, lift a coiled chain to full extension, and lift a leaky bucket (Example #4, #5, and #6)
- Finding work needed to pump water out of a cylindrical tank (Example #7)
Hydrostatic Force
1 hr 51 min 9 Examples
- Introduction to Video: Hydrostatic Force
- Overview of Hydrostatic Force exerted on an object
- Find the fluid force of a rectangular plate submerged even to surface (Example #1)
- Find the fluid force of a triangular plate submerged even to surface (Example #2)
- Determine the fluid force of a trapezoidal plate submerged even to surface (Example #3)
- Determine the fluid force of a semicircular plate submerged even to surface (Example #4)
- Determine the fluid force of a parabolic plate submerged even to surface (Example #5)
- Find hydrostatic force of a square plate submerged below the water’s surface (Example #6)
- Find hydrostatic force of a right triangular plate submerged below the water’s surface (Example #7)
- Determine the hydrostatic force of a square plate submerged below the surface (Example #8)
- Find hydrostatic force against the semicircular gate of partially submerged dam (Example #9)
Moments and Center of Mass
34 min 2 Examples
- Overview of what is the Center of Mass (centroid) and Moments
- Example #1 of finding the center of mass using integration by parts
- Example #2 of finding the center of mass using Integration by Parts and Half-Angle Identity
Chapter Test
2 hr 44 min 24 Examples
- 24 Challenging Practice Problems
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment