{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 8 InverseTrigFunctions-Integration

# Lesson 8 InverseTrigFunctions-Integration - the arctan...

This preview shows pages 1–11. Sign up to view the full content.

INTEGRATION OF INVERSE TRIGONOMETRIC FUNCTIONS

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Review Recall derivatives of inverse trig functions 2 1 2 1 2 1 2 1 sin , 1 1 1 tan 1 1 sec , 1 1 d du u u dx dx u d du u dx u dx d du u u dx dx u u - - - = < - = + = < -
Integrals Using Same Relationships 3 2 2 2 2 2 2 arcsin 1 arctan 1 arcsec du u C a a u du u C a u a a du u C a a u u a = + - = + + = + - When given integral problems, look for these patterns

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
. If a=1, you have: 1. + = - - C u sin u 1 du 1 2 2. + = + - C u tan u 1 du 1 2 3. + = - - C u u u du 1 2 sec 1
Identifying Patterns For each of the integrals below, which inverse trig function is involved? 5 2 4 13 16 dx x + 2 25 4 dx x x - 2 9 dx x -

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Warning Many integrals look like the inverse trig forms Which of the following are of the inverse trig forms? 6 2 1 dx x + 2 1 x dx x + 2 1 dx x - 2 1 x dx x - If they are not, how are they integrated?
Try These Look for the pattern or how the expression can be manipulated into one of the patterns 7 2 8 1 16 dx x + 2 1 25 x dx x - 2 4 4 15 dx x x - + + 2 5 10 16 x dx x x - - +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Completing the Square Often a good strategy when quadratic functions are involved in the integration Remember … we seek (x – b) 2 + c Which might give us an integral resulting in

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the arctan function 2 2 10 dx x x + + âˆ« Completing the Square â€¢ Try these 2 2 2 4 13 dx x x-+ + âˆ« 2 2 4 dx x x-+ âˆ« Example : Evaluate the following integrals using the formulas for integrals yielding inverse trigonometric functions: âˆ«-2 5 2 . 1 s ds âˆ«-2 2 . 2 x x dx âˆ«--2 3 . 3 2 x x dx âˆ«-9 16 . 4 2 y y dy âˆ« + + 1 . 5 2 x x xdx ( 29 âˆ« + + + 3 4 2 3 . 6 2 x x x dx ( 29 âˆ« + +-3 2 2 1 3 . 7 2 x x dx x HOMEWORK : Evaluate the following integral . 11 âˆ«-4 9 16 . 1 r rdr âˆ«-x xdx 2 cos 2 sin . 2 ( 29 âˆ« + x x dx 1 . 3 âˆ« + + dx x x 2 2 4 1 . 4 âˆ«-dx e e x x 2 1 . 5 âˆ«--2 2 3 . 6 x x xdx Î¸ d âˆ« + 2 sin 1 cos . 7 âˆ« +-3 4 2 2 . 8 2 3 x x dx x ( 29 [ ] âˆ« + 2 ln 1 . 9 x x dx âˆ«-1 9 . 10 2 x x dx âˆ«-1 2 2 . 11 t dt âˆ«-+ 1 2 / 1 2 4 4 3 . 12 dx x x âˆ«--3 ln 2 ln . 13 z z e e dz...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern