CK-12-Calculus

7.2. Integration By Parts http://www.ck12.org ; Math Video Tutorials by James Sousa, Integration by Parts (10:03) MEDIA Click im ...

http://www.ck12.org Chapter 7. Integration Techniques 7.3 Integration by Partial Fractions Learning Objectives A student will be ...

7.3. Integration by Partial Fractions http://www.ck12.org 2 x− 19 x^2 +x− 6 = A x+ 3 + B x− 2. Our goal at this point is to find ...

http://www.ck12.org Chapter 7. Integration Techniques For each distinct factorax+b,the right side must include a term of the fo ...

7.3. Integration by Partial Fractions http://www.ck12.org ∫ x+ 1 (x+ 2 )^2 dx= ∫( 1 x+ 2 − 1 (x+ 2 )^2 ) = ∫ 1 x+ 2 dx− ∫ 1 (x+ ...

http://www.ck12.org Chapter 7. Integration Techniques Now we have solved forA,B,andC.We use the partial fraction decomposition t ...

7.3. Integration by Partial Fractions http://www.ck12.org ∫ 2 1 x^3 − 4 x^2 − 3 x+ 3 x^2 − 3 x dx= ∫ 2 1 [ (x− 1 )+−x (^26) −x+ ...

http://www.ck12.org Chapter 7. Integration Techniques Review Questions Evaluate the following integrals. 1.∫x (^21) − 1 dx 2.∫x ...

7.4. Trigonometric Integrals http://www.ck12.org 7.4 Trigonometric Integrals Learning Objectives A student will be able to: Com ...

http://www.ck12.org Chapter 7. Integration Techniques ∫ cos^2 xdx= ∫ 1 2 (^1 +cos 2x)dx =^12 ∫ ( 1 +cos 2x)dx =^12 ( x+^12 sin 2 ...

7.4. Trigonometric Integrals http://www.ck12.org =−cosx− ∫ [ −u^2 sinxsindux ] =−cosx+ ∫ u^2 du =−cosx+u 3 3 +C =−cosx+^13 cos^3 ...

http://www.ck12.org Chapter 7. Integration Techniques Example 5: Evaluate∫sin^4 xcos^4 xdx. Solution: Here,m=n= 4 .We follow the ...

7.4. Trigonometric Integrals http://www.ck12.org ∫ tanxdx= ∫ sinx cosxdx. Usingu−substitution, letu=cosx,sodu=−sinxdx.The integr ...

http://www.ck12.org Chapter 7. Integration Techniques Example 7: Evaluate∫tan^5 xdx. Solution: We use the formula above by subst ...

7.4. Trigonometric Integrals http://www.ck12.org Now we make theu−substitution: = ∫ u^2 (u^2 + 1 )du =^15 u^5 +^13 u^3 +C =^15 t ...

http://www.ck12.org Chapter 7. Integration Techniques ; see Trigonometric Integrals, Part 3 (5:54) MEDIA Click image to the left ...

7.4. Trigonometric Integrals http://www.ck12.org 6.∫tan^4 xsecxdx 7.∫√tanxsec^4 xdx 8.∫ 0 π/^2 tan^5 x 2 dx Graph and then find ...

http://www.ck12.org Chapter 7. Integration Techniques 7.5 Trigonometric Substitutions Learning Objectives A student will be able ...

7.5. Trigonometric Substitutions http://www.ck12.org In the second column are listed the most common substitutions. They come fr ...

http://www.ck12.org Chapter 7. Integration Techniques since cotθ=cossinθθ. so that ∫ dx x^2 √ 4 −x^2 =− 1 4 cotθ+C =−^14 √ 4 −x^ ...