Department of Mathematics
University of California, Santa Barbara
Math 3B
Differential and Integral Calculus II
| Video Library | Series of videos explaining approximation of area under a curve |
| Video - 6:15 | Calculating a definite integral using the limit definition |
| Interactive | Visualization of the Riemann sum | Try varying left/right/mid and the number of intervals |
| Text | Examples of computing definite integrals from the definition |
| Video - 3:15 | Example of a definite integral using only geometry |
| Video - 8:03 | First FTC explained |
| Video - 12:23 | Nice illustration of the Second FTC |
| Video - 3:54 | Examples using First FTC and chain rule | Other types of examples in the next two videos |
| Text | Early examples of the Second FTC |
| Interactive | Visualization of the First FTC | They say "second" FTC when they mean "first" |
| Text | The basic antiderivative formulas |
| Video Library | Several videos with examples of u-substitution |
| Text | Lots of u-substitution examples |
| Video - 10:03 | Harder u-substitution examples |
| Interactive | Visualization of u-substitution |
| Video Library | Several video with examples of integration by parts |
| Text | Lots of integration by part examples |
| Text | Lots of examples of integrals of product of trig functions |
| Video - 8:56 | Very good explanation of integrals of trig functions | See next few videos for more examples |
| Video - 5:57 | Integrals of trig functions | See next few videos for more examples |
| Video Library | Several videos with examples of trig substitution |
| Text | Lots of examples of integrals using trig substitution |
| Text | Lots of examples of integrating rational functions |
| Video - 19:35 | Explanation of partial fraction decomposition | See next few videos to see the actual integrals |
| Video Library | Several videos explaining improper integrals |
| Text | Lots of examples of improper integrals |
| Interactive | Really nice visualization of improper integrals |
| Video - 4:09 | Simple area between curves example | See next video as well |
| Text | Complete explanation of area between curves |
| Video Library | Lots of videos explaining how to find the volume of solids of revolution |
| Text | Washer/disc method |
| Text | Cylindrical shell method |
| Text | Cross-sectional volume methods |
| Interactive | Visualization of washer/disc method |
| Interactive | Visualization of cross-sectional volume method |
| Text | Explanation and examples of arc length |
| Video - 7:08 | Explanation and example of arc length | See next video for a harder example |
| Interactive | Visualization of arc length |
| Text | Explanation and examples of surface area |
| Video - 9:47 | Explanation and examples of surface area | See next video for more examples |
| Text | Finding the average value of a function |
| Video - 3:33 | How to find average value of a function | See next video as well |
| Text | Using integration to find hydrostatic pressure |
| Text | Finding the center of mass of a region of the plane |
| Video - 5:54 | Center of mass examples | See next video as well |
| Text | Using integration to calculate work |
| Video - 5:00 | Hooke's Law - example1 | See next video as well |
| Video - 9:02 | Finding work using integral - example1 (cable/rope problem) | See next video as well |
| Video - 10:27 | Finding work using integral - example1 (pumping problem) |
