Page 228 - Calculus Workbook For Dummies

212 Part IV: Integration and Infinite Series

p # x 9 - 25 x dx = - 1 _ 9 - 25 x i / 3 2 + C
2
2
75
1. Rewrite as # x 3 - ^ 5 xh 2 dx.
2
2. Do the triangle thing. See the following figure.

3
5x

θ

√9 − 25x 2
5 x
3. Solve sin =i for x then get dx.
3
3 3
i
x = sini dx = cos di
5 5
4. Do the Radically Awesome thing.
9 - 25 x 2 2
3 = cosi 9 - 25 x = 3 cosi
5. Substitute.
# x 9 - 25 x dx
2
3 3 27 # 2
i
i
= # c sini ^ m 3 cosi c h cos dim = cos i sin di
5 5 25
27 1 3 9 3
6. Integrate: = c - cos im + C = - cos i + C .
25 3 25 J 2 N 3
9 K 9 - 25 x O 1 2 / 3 2
7. Switch back to x (look at Step 4): = - K O + C = - _ 9 - 25 x i + C .
25 3 75
L P
q # dx = 1 ln 25 + 625 x - 121 + C
2
x
625 x - 121 25
2
1. Rewrite as # dx .
2 2
x -
^ 25 h 11
u
2. Do the triangle thing. For this problem, sec =i a . See the following figure.
25x
2
√625x − 121

θ

11
25 x
3. Solve sec =i for x and find dx.
11
11 11
i
i
x = seci dx = sec tan di
25 25