5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:52

232 STEP 4. Review the Knowledge You Need to Score High

Example 9

Evaluate

∫

sinx− 1

cos

dx.

Rewrite as

∫(

sinx

cosx

−

1

cosx

)

dx=

∫

(tanx−secx)dx=

∫

tanxdx−

∫

secxdx

=ln|secx|−ln|secx+tanx|+C=ln

∣

∣∣

∣

secx

secx+tanx

∣

∣∣

∣+C

or−ln|sinx+ 1 |+C.

Example 10

Evaluate

∫

e^2 x

ex

dx.

Rewrite as

∫

exdx=ex+C.

Example 11

Evaluate

∫

3

1 +x^2

dx.

Rewrite as 3

∫

1

1 +x^2

dx=3 tan−^1 x+C.

Example 12

Evaluate

∫

1

√

9 −x^2

dx.

Rewrite as

∫

1

√

32 −x^2

dx=sin−^1

(

x

3

)

+C.

Example 13

Evaluate

∫

7 xdx.

∫

7 xdx=

7 x

ln 7

+C

KEY IDEA

Reminder: You can always check the result by taking the derivative of the answer.

TIP • Be familiar with the instructions for the different parts of the exam before the day of

the exam. Review the instructions in the practice tests provided at the end of this book.