CK-12-Calculus

6.5. Derivatives and Integrals Involving Inverse Trigonometric Functions http://www.ck12.org To change the limits, x=ln 2→u=e−x= ...

http://www.ck12.org Chapter 6. Transcendental Functions ; Math Video Tutorials by James Sousa, Integration Involving Inverse Tri ...

6.6. L’Hospital’s Rule http://www.ck12.org 6.6 L’Hospital’s Rule Learning Objectives A student will be able to: Learn how to fi ...

http://www.ck12.org Chapter 6. Transcendental Functions limx→ 0 √ 2 +x−√ 2 x =limx→ 0 [d dx( √ 2 +x−√ 2 ) dxd(x) ] = [ 1 /( 2 √ ...

6.6. L’Hospital’s Rule http://www.ck12.org A broader application of L’Hospital’s rule is whenx=ais substituted into the derivati ...

http://www.ck12.org Chapter 7. Integration Techniques CHAPTER 7 Integration Techniques Chapter Outline 7.1 Integration by Substi ...

7.1. Integration by Substitution http://www.ck12.org 7.1 Integration by Substitution Each basic rule of integration that you hav ...

http://www.ck12.org Chapter 7. Integration Techniques Learning Objectives A student will be able to: Compute by hand the integr ...

7.1. Integration by Substitution http://www.ck12.org Example 1: Evaluate∫(x+ 1 )^5 dx. Solution: Letu=x+ 1 .Thendu=d(x+ 1 ) = 1 ...

http://www.ck12.org Chapter 7. Integration Techniques Trigonometric Integrands We can apply the change of variable technique to ...

7.1. Integration by Substitution http://www.ck12.org ∫ 1 cos^23 xdx= ∫ sec^23 xdx. Substituting for the argument of the secant,u ...

http://www.ck12.org Chapter 7. Integration Techniques Using Substitution on Definite Integrals Example 6: Evaluate∫ 13 √ 2 xx− 1 ...

7.1. Integration by Substitution http://www.ck12.org Let’s try the substitution method of definite integrals with a trigonometri ...

http://www.ck12.org Chapter 7. Integration Techniques 2.∫√ 2 +xdx 3.∫ √ 21 +xdx 4.∫xx+^21 dx 5.∫e−e−x+x 2 dx 6.∫^3 √t+ 5 t dt 7. ...

7.2. Integration By Parts http://www.ck12.org 7.2 Integration By Parts Learning Objectives A student will be able to: Compute b ...

http://www.ck12.org Chapter 7. Integration Techniques Evaluate∫xsinxdx. Solution: We use the formula∫udv=uv−∫vdu. Choose u=x and ...

7.2. Integration By Parts http://www.ck12.org As you can see, this integral is worse than what we started with! This tells us th ...

http://www.ck12.org Chapter 7. Integration Techniques Solution: Here, we only have one term, lnx.We can always assume that this ...

7.2. Integration By Parts http://www.ck12.org Tabular Integration by Parts Sometimes, we need to integrate by parts several time ...

http://www.ck12.org Chapter 7. Integration Techniques ∫ excosxdx=exsinx− [ −excosx− ∫ (−cosx)(exdx) ] =exsinx−excosx− ∫ excosxdx ...