# U-Substitution Homework Master Math Mentor Answers For Interview

## AB Calculus Manual (Revised 1/2016)

This page provides the AB Calculus Manual for the classroom - all chapters of this manual are provided as free downloads! This section is a complete high school course for preparing students to take the AB Calculus exam.

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In addition to the Essentials section of the manual that provide complete coverage of all topics for the AB exam, there is a Non-Essentials section as well that givers topics that are relevant to AB calculus but not on the actual AP exam. There is also a Review section that goes over the most common algebraic concepts that give students trouble.

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This manual can easily replace an expensive textbook. Teachers teach right from it and students write in it.

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The Solution Manual is exactly the same as the student manual except that the solutions with all important steps are shown. There is a one-to-one relationship between the pages of the student manual and the solution manual. So, for example, page 73 will have a series of problems and blank space for the students to write in the solutions. The solution manual's page 73 will have the same problems but with the solutions shown.

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New: In addition, a set of answer pages (no shown work, just the answer) comes with the solution manual.Â It is also available in download form as a stand-alone product.

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AB Calc Cover Pages ABSolutionsp000Cover.pdf Â 0.5MB | Download Free |

Essentials | |

Pages 1-26 01. Introduction 02. Tangent Lines 03. Slope secant/tangent 04. Limits graphical 05. Limits Algebraic ABStudentsp001-026.pdf Â 4.4MB | Download Free |

Pages 27-46 06. Derivative definition 07. Derivatives w/ technology 08. Differentiation techniques 09. Chain Rule ABStudentsp027-046.pdf Â 4.6MB | Download Free |

Pages 47-69 10. Derivatives of trig functions 11. Implicit differentiation 12. Derivatives transcendentals 13. Derivatives of inverses 14. Linear approximations ABStudentsp047-069.pdf Â 4.4MB | Download Free |

Pages 70-93 15. Continuity/differentiability 16. Related rates ABStudentsp070-093.pdf Â 2.5MB | Download Free |

Pages 94-121 17. Straight-line motion 18. 3 important theorems 19. Function analysis ABStudentsp094-121.pdf Â 4.5MB | Download Free |

Pages 122-151 20. Curve sketching 21. Absolute extrema 22. Optimization 23. Economic optimization 24. L'Hospital's rule ABStudentsp122-151.pdf Â 3.3MB | Download Free |

Pages 152-170 25. Indefinite integration 26. u-substitution27. Riemann sums ABStudentsp152-170.pdf Â 3.9MB | Download Free |

Pages 171-184 28. Definite integrals 29. Accumulation function 30. Fundamental Theorem ABStudentsp171-184.pdf Â 3.8MB | Download Free |

Pages 185-198 31. Definite integrals u-sub32. Integrating transcendentals 33. Motion revisited ABStudentsp185-198.pdf Â 2.3MB | Download Free |

Pages 199-212 34. Average value, 2nd FTC 35. Inverse Trig 36. Area between curves ABStudentsp199-212.pdf Â 3.2MB | Download Free |

Pages 213-240 38. Integral Applications (just added) ABStudentsp213-240.pdf Â 3.6MB | Download Free |

Non-Essentials | |

Pages 241-265 1a. Introduction 12a. Logarithmic differentiation 14a. Differentials 24a. Newton's method 26a. L'Hospital advanced 29a. Exact area w/limits 37a. Volume shells ABStudentsp241-265NonEss.pdf Â 5.1MB | Download Free |

Review | |

Pages 266-276 Complex fractions Inverses Exponentials/logs Graphical solutions Sigma notation ABStudentsp266-276Review.pdf Â 3.4MB | Download Free |

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**Next:**About this document ...

### SOLUTIONS TO U-SUBSTITUTION

*SOLUTION 1 :*Integrate . Let

*u* = *x*^{2}+5*x*

so that

*du* = (2*x*+5) *dx* .

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

* SOLUTION 2 :* Integrate . Let

*u* = 3-*x*

so that

*du* = (-1) *dx* ,

or

(-1) *du* = *dx* .

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

* SOLUTION 3 :* Integrate . Let

*u* = 7*x*+9

so that

*du* = 7 *dx* ,

or

(1/7) *du* = *dx* .

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

* SOLUTION 4 :* Integrate . Let

*u* = 1+*x*^{4}

so that

*du* = 4*x*^{3}*dx* ,

or

(1/4) *du* = *x*^{3}*dx* .

Substitute into the original problem, replacing all forms of *x*, getting

(Do not make the following VERY COMMON MISTAKE : . Why is this INCORRECT ?)

.

Click HERE to return to the list of problems.

* SOLUTION 5 :* Integrate . Let

*u* = 5*x*+2

so that

*du* = 5 *dx* ,

or

(1/5) *du* = *dx* .

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

* SOLUTION 6 :* Integrate . Let

*u* = 3*x*

so that

*du* = 3 *dx* ,

or

(1/3) *du* = *dx* .

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

* SOLUTION 7 :* Integrate . Let

so that

.

Substitute into the original problem, replacing all forms of *x*, getting

.

Click HERE to return to the list of problems.

*Duane Kouba*

*1999-05-07*