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1 AP Eam Practice Questions for Chapter 7 AP Eam Practice Questions for Chapter 7. e e So, the answer is A. e e ( ) A e e d e e e e (, ) + (, ) (, ) ( ) ( ),, A d d ( 7 ) ( ) ( ) ( 7 ) ( ) 7 ( 7 ) d ( 7 ) d So, the answer is C. π. ( cos sin ) A d [ sin cos] + π + + () So, the answer is A.. sin sin π π A ( sin ) [ cos ] + π π + + π + So, the answer is B. d Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

2 AP Eam Practice Questions for Chapter 7. Write both equations in terms of and find the points of intersection. + +, ( )( ) ( ) ( ) ( ) d A d ( ) ( ) So, the answer is D.. ln ( sec ) 7. d sec tan d sec tan π s + tan d π π (, ) (, ) sec sec d d So, the answer is B.. e d.( e ) e d... ( ) s + e d + e d So, the answer is A d d s + d + d ( + ) ( 7 ) So, the answer is B. s + d + d d d ( ) d + C Use (, 9) to find C. () 9 + C 9 + C C 7 d The equation for the curve is + 7. So, the answer is A. V sin d. So, the answer is C. Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

3 AP Eam Practice Questions for Chapter 7. (a) (, ) k Find the point of intersection of the graphs k.77 ( + ) ( + ) d k d or + + k d d Notes: Use our calculator to find the point of intersection of the two graphs (no work needed for this). In this intermediate step, round the -coordinate of the intersection point to more than three decimal places to use in upcoming integrals. (b) + 9 ( ) s + d ( ) + ( ). d Notes: Be sure to write down the appropriate definite integral before numericall approimating it on our calculator. places to receive credit on the eam. (c) A w h ( ) ( ) + + ( ) 9.77 V 9 d.9 Notes: Be sure to write down the appropriate definite integral before numericall approimating it on our calculator. places to receive credit on the eam. Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

4 AP Eam Practice Questions for Chapter 7. (a) The graphs intersect at. and A ln d.7 Notes: Use our calculator to find the points of intersection of the two graphs (no work needed for this). In this intermediate step, round the coordinates of the intersection points to more than three decimal places to use in upcoming integrals. ( ln ).799 (b) π V + + d.7. Notes: Be sure to write down the appropriate definite integral before numericall approimating it on our calculator. places to receive credit on the eam. (c) Rewrite the equations in terms of. ln e + The graphs intersect at.7 and π ( e ) d.7 Notes: To use the disk method (washer method), set up this integral in terms of (using horizontal elements in R). Setting up the volume integral in terms of (using vertical elements in R) requires the shell method. Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

5 AP Eam Practice Questions for Chapter 7. (a) Find the points of intersection of the graphs ± ,.7 ( ) ( ).79 A + d +.77 Notes: It is strategic to set up this area integral in terms of. Setting up the area integral in terms of requires the sum of multiple definite integrals. Use our calculator to find the points of intersection of the two graphs (no work needed for this). In this intermediate step, round the coordinates of the intersection points to more than three decimal places to use in upcoming integrals. Be sure to write down the appropriate definite integral before numericall approimating it on our calculator. places to receive credit on the eam. (b).7 ( ) ( + ) V π d (c) π ( + )( + ) π d or.79. ( + ) ( + ) d ( ).9 + π + d. Notes: To use the disk method (washer method), set up this integral in terms of. Setting up this volume integral in terms of, via the shell method, requires the sum of multiple definite integrals. Be sure to write down the appropriate definite integral before numericall approimating it on our calculator. places to receive credit on the eam. Notes: It is strategic to set up the shell method here in order to set up a single integral. Setting up this volume integral in terms of, via the disk/washer method, requires the sum of multiple definite integrals. Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

6 AP Eam Practice Questions for Chapter 7. (a) pts: sketch of correct region (with boundar curves labeled) + + (b) A + d d Notes: It is strategic to set up this area integral in terms of. Setting up this area integral in terms of requires the sum of multiple definite integrals. The answer does not need to be simplified. V d d π π π π. (a) (b) π V d ( ) π π π d Notes: To use the disk method (washer method), set up this integral in terms of. Setting up the volume integral in terms of requires the shell method. (c) π ( + ) ( ) d π + d pts: integral Notes: To use the disk method (washer method), set up this integral in terms of. Setting up the volume integral in terms of requires the shell method. A bh (d) V d Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

7 AP Eam Practice Questions for Chapter 7 7. (, ) (, ) R S (a) ( ) A d (b) π ( ) π ( ) V d or d π 9π 9π V π d π π d Notes: To use disks, set up this integral terms of. Setting up the volume integral in terms of requires the shell method. (c) A V π π π d π 7 7 π π 7 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

8 AP Eam Practice Questions for Chapter 7 7. T (a) ( + ) d A d + + (b) π ( ) ( [ ]) ( ) ( ) π ( + + ) d V d π d π + + π + + 7π (c) P ( ) + ( ) + ( ) + ( ) d d Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

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