1,001 Calculus Practice Problems For Dummies
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Chapter 10: The Fundamental Theorem of Calculus
and the Net Change Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
The Problems You’ll Work On ..................................................................... 79
What to Watch Out For ................................................................................. 79
Using the Fundamental Theorem of Calculus
to Find Derivatives ..................................................................................... 80
Working with Basic Examples of Definite Integrals ................................... 80
Understanding Basic Indefinite Integrals ................................................... 81
Understanding the Net Change Theorem ................................................... 84
Finding the Displacement of a Particle Given the Velocity ...................... 85
Finding the Distance Traveled by a Particle
Given the Velocity ...................................................................................... 85
Finding the Displacement of a Particle Given Acceleration ..................... 86
Finding the Distance Traveled by a Particle
Given Acceleration ..................................................................................... 86
Chapter 11: Applications of Integration . . . . . . . . . . . . . . . . . . . . . . . . . .87
The Problems You’ll Work On ..................................................................... 87
What to Watch Out For ................................................................................. 87
Areas between Curves .................................................................................. 88
Finding Volumes Using Disks and Washers ............................................... 89
Finding Volume Using Cross-Sectional Slices ............................................ 91
Finding Volumes Using Cylindrical Shells .................................................. 92
Work Problems .............................................................................................. 94
Average Value of a Function ......................................................................... 97
Chapter 12: Inverse Trigonometric Functions,
Hyperbolic Functions, and L’Hôpital’s Rule . . . . . . . . . . . . . . . . . . . . . .99
The Problems You’ll Work On ..................................................................... 99
What to Watch Out For ................................................................................. 99
Finding Derivatives Involving Inverse
Trigonometric Functions ........................................................................ 100
Finding Antiderivatives by Using Inverse
Trigonometric Functions ........................................................................ 101
Evaluating Hyperbolic Functions Using Their Definitions ..................... 101
Finding Derivatives of Hyperbolic Functions ........................................... 102
Finding Antiderivatives of Hyperbolic Functions .................................... 102
Evaluating Indeterminate Forms Using L’Hôpital’s Rule ........................ 103
Chapter 13: U-Substitution and Integration by Parts . . . . . . . . . . . . . .107
The Problems You’ll Work On ................................................................... 107
What to Watch Out For ............................................................................... 107
Using u-Substitutions .................................................................................. 108
Using Integration by Parts .......................................................................... 109