# AC6.6 - 6.6 CONCEPT QUESTIONS page 458 1 b a f x g x dx 2 b...

This preview shows pages 1–6. Sign up to view the full content.

6 Integration 561 6.6 CONCEPT QUESTIONS, page 458 1. [() () ] b a f xg x d x 2. [ ( ) ( )] [ ( ) ( )] [ ( ) ( )] bcd abc fx gxd x gx fxd x x −+−+ ∫∫∫ EXERCISES 6.6, page 458 1. −− = += z () ( ) ( ) xx d x 32 43 0 6 0 6 6 2 6 2 6 108 1 4 1 4 sq units. 2. = −= = z d xxx 45 0 2 0 2 28 1 2 1 5 32 5 8 5 sq units. 3. A x xd x x x x x d x =− + = z zz 11 2 1 22 0 1 1 0 212 0 1 / (by symmetry). Let u = 1 x 2 so that du = 2 x dx or x dx = - 1 2 du . Also, if x = 0, then u = 1 and if x = 1, u = 0. So 0 1 1/2 3/2 12 2 2 23 3 3 0 1 (2)( ) , or sq unit. A u du u = = 4. A x x dx x x dx x x dx x + + + = + =+ X Z Y z z 2 4 2 4 2 2 4 24 2 0 2 2 0 2 0 2 2 0 ln( ) = (ln 8 ln 4)2 = ln 4 sq units. 5. Ax x d x d x x x = − + + z z ( ) // 2 0 4 0 4 0 4 1 2 4 3 = 8 + 32 3 8 3 = sq units. 6. x d x x x d x x x x = + + z z [( ) ] ( )( ) 2 2 0 4 0 4 0 4 2 3 1 2 = 16 3 16 3 88 −+= .

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

View Full Document
6 Integration 562 7. The required area is given by () // / / x x dx x x dx x x x x 21 3 1 0 13 2 3 43 1 0 3 0 1 0 1 1 3 3 4 3 4 1 3 −+ = + zz = −+−= ( ) 1 3 3 4 3 4 1 3 1 2 1 sq units. 8. Ax x d x xx d x =+ + + z z [( ) ( )] [( ) ] 66 1 2 3 0 2 4 0 + + z z [ ( ) ] 3 2 3 0 2 4 0 xd x x x d x = 3 4 2 4 0 1 2 2 1 4 4 0 2 6 6 12 24 2 12 4 22 x +++ = + + = ( ) ( ) ( ) sq units. 9. The required area is given by −− = =+= z x x 2 1 2 3 1 2 1 3 8 3 1 3 3 sq units. 10. d x x d x =− z z 22 0 2 2 2 42 4 =− + =−+ 24 2 8 1 3 8 3 3 0 2 ( ) 11. y = x 2 5 x + 4 = ( x 4)( x 1) = 0 if x = 1 or 4. These give the x- intercepts. x d x x x x + + z 2 1 3 3 5 2 2 1 3 1 3 54 4 =−+ − −− + − = = ( ) . 91 2 4 3 45 2 1 3 5 2 10 3 1 3 = 32 3 sq units .
6 Integration 563 12. The required area is given by −= = + = z xd x x 34 1 0 1 0 1 4 1 4 1 4 1 4 01 () . 13. The required area is given by −−+ =+ =+ = z . / 1 9 18 27 2 3 32 0 9 0 9 x x x 14. Ax x d x x x =− + z // 1 2 1 4 2 3 12 2 0 4 0 4 15. −− = z ed x e xx (/ ) 2 4 2 -2 4 =−+ = 4 16 3 4 3 sq units. 2 21 ee sq units.

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

View Full Document
6 Integration 564 16. Ax e d x x e d x xx =− − = −− z z 22 0 1 0 1 . Let u = x 2 so that du = 2 x dx or x dx = - 1 2 du . Also, if x = 0, then u = 0 and if x = 1 then u = 1. So Ae d u e uu =− z 1 2 1 2 0 1 0 1 17. d x =+ z [( ) ] 2 1 3 31 = () (). 96 2 1 3 38 3 +−+= 18. xd x z [( ) ( )] 24 2 1 2 + + 1 3 1 2 32 1 2 6 x 19. x x d x ++ + z 2 0 2 23 3 + + 1 3 3 2 1 3 3 2 0 2 4 (8) ( ) 20. The region is shown in the figure on the right. + = 1 2 1 2 1 2 11 1 ee . sq units = + z x x x 2 1 3 3 1 3 1 3 + + z d x 2 1 2 6 =− + + − + − = ( ) 8 3 1 3 1 2 1 2 2 12 6 16 sq units + z d x 2 0 2 3 =−= 6 8 3 10 3 sq units
6 Integration 565 Ax x d x =− + z [( ) ( )] 92 3 2 1 1 = −− + 1 3 32 1 1 6 xx x 21. x d x =+ z [( ) ] 23

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.

{[ snackBarMessage ]}

### Page1 / 16

AC6.6 - 6.6 CONCEPT QUESTIONS page 458 1 b a f x g x dx 2 b...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online