**Ch 8 - Integration Techniques & L'Hopital's Rule**

**Chapter 8 PDF Resource**

calculus_chapter_8.pdf |

**Lecture Notes & Videos**

Section 8-2 (Day 1)

Integration by Parts

-----VIDEO: Integration by Parts

-----VIDEO: How To Pick "u" and "dv" When Doing Integration by Parts?

Section 8-2 (Day 2)

Integration by Parts Short-Cut

-----VIDEO: Short-Cut Trick for Integration By Parts

Section 8-7

L'Hopital's Rule

-----VIDEO: L'Hopital's Rule

Integration by Parts

-----VIDEO: Integration by Parts

-----VIDEO: How To Pick "u" and "dv" When Doing Integration by Parts?

Section 8-2 (Day 2)

Integration by Parts Short-Cut

-----VIDEO: Short-Cut Trick for Integration By Parts

Section 8-7

L'Hopital's Rule

-----VIDEO: L'Hopital's Rule

**Worksheets**

**Interactive Animations**

Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.

**Please be patient! It takes awhile for these to load.**

Widen the browser, if necessary, to see the entire animation.

Widen the browser, if necessary, to see the entire animation.

**Visualizing L'Hopital's Rule**

Move the slider and observe that the ratio of the slopes of the tangent lines approaches the ratio of the values of the functions at the x-intercepts.

As the tangent lines approach each x-intercept, can you see how the ratio of their slopes ought to be a close approximation of the ratio of their values as L'Hopital's Rule would indicate?

Type new functions if you like, but if you do, the tangent lines may not keep up with you.

To fix this, (1) move the slider, then (2) click the undo button.

Then the tangent lines should catch up with you.

As the tangent lines approach each x-intercept, can you see how the ratio of their slopes ought to be a close approximation of the ratio of their values as L'Hopital's Rule would indicate?

Type new functions if you like, but if you do, the tangent lines may not keep up with you.

To fix this, (1) move the slider, then (2) click the undo button.

Then the tangent lines should catch up with you.