8.3 Trigonometric Integrals

Objectives

  • Evaluate integrals involving powers of sines and cosines.
  • Evaluate integrals involving square roots of sines and cosines.
  • Evaluate integrals involving powers of tangents and secants.
  • Evaluate integrals involving products of sines and cosines.
  • Evaluate trigonometric integrals using a variety of methods.
  • Use trigonometric integrals to find areas, volumes, centroids, average values, or arc lengths.

Readings and Lecture Videos

8.3 Trigonometric Integrals.pptx Download 8.3 Trigonometric Integrals.pptx

8.3 Trigonometric Integrals.pdf Download 8.3 Trigonometric Integrals.pdf  

Example 1 odd power of sine:  https://mediaplayer.pearsoncmg.com/assets/teu14_8_3_1 Links to an external site.

Example 2 odd power of cosine:  https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=3 Links to an external site.

Example 3  Integrate the product of an even power of cosine and an even power of sine:  https://mediaplayer.pearsoncmg.com/assets/teu14_8_3_3 Links to an external site.

Example 4 power-reducing formulas:  https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=5 Links to an external site.

Example 5 Integrate an even power of tangent: https://mediaplayer.pearsoncmg.com/assets/teu14_8_3_5 Links to an external site.

Example 6: Integrate an odd power of secant:

https://mediaplayer.pearsoncmg.com/assets/teu14_8_3_6 Links to an external site.

When you use integration by parts, you can use the tabular method:

IMG_9173.jpg

Example 7 integrate the powers of tangent and secant: https://mediaplayer.pearsoncmg.com/assets/teu14_8_3_7 Links to an external site.

Checkpoint 7: Integrate even power of secant: https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=6 Links to an external site.

Products of sines and cosines:  https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=7 Links to an external site.

(I will provide you with these formulas on the test.)

Example 8 product of two cosines: https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=8 Links to an external site.

Example 9 product of sine and cosine: https://mediaplayer.pearsoncmg.com/assets/teu14_sl_0803?clip=9 Links to an external site.