Page 227 - Calculus Workbook For Dummies

211
Chapter 11: Integration Rules for Calculus Connoisseurs

4. Do the a thing.
2
9 x + 4 seci 2 seci
2 = 9 x + 4 = 2
5. Substitute.
# dx 3
2
9 x + 4
2 sec i di
2
= # 3 3 = 1 # di = 1 # cos di
i
2 ^ secih 12 seci 12
1
i
6. Integrate to get = sin + C .
12
7. Switch back to x (use the triangle).
J N
1 K 3 x O x
= 12 K 2 O + C = 2 + C
L 9 x + 4 P 4 9 x + 4
o # xdx = - 25 - x + C
2
25 - x 2
1. Rewrite as # xdx .
2
5 - x 2
u
2. Draw your triangle. For this problem, sin =i a . See the following figure.

5
x

θ

√25 − x 2
3. Solve sin =i x for x, and then get dx.
5
i
x = 5 sini dx 5 cos di
=
4. Do the a thing.

25 - x 2 cosi 2 cosi
5 = 25 - x = 5
5. Substitute.

# xdx
25 - x 2
i
= # 5 ^ sini ^h 5 cos dih = 5 # sin di
i
5 cosi
i
6. Integrate to get 5 cos + C .
-
J 2 N
7. Switch back to x (look at Step 4): = - K K 25 - x O O + C = - 25 - x + C
2
5
L 5 P