242 STEP 4. Review the Knowledge You Need to Score High
Example 3Evaluate∫− 1− 8(√ (^3) y+ 1
√ (^3) y
)
dy.
Rewrite:
∫− 1
− 8
(
y^1 /^3 +
1
y^1 /^3)
dy=∫− 1− 8(
y^1 /^3 +y−^1 /^3)
dy=
y^4 /^3
4 / 3+
y^2 /^3
2 / 3]− 1− 8=
3 y^4 /^3
4+
3 y^2 /^3
2]− 1− 8=(
3(−1)^4 /^3
4+
3(−1)^2 /^3
2
)−
(
3(−8)^4 /^3
4+
3(−8)^2 /^3
2
)=
(
3
4+
3
2
)
−(12+6)=− 63
4
.
Verify your result with a calculator.
TIP • You may bring up to 2 (but no more than 2) approved graphing calculators to the
exam.Definite Integrals Involving Absolute ValueExample 1Evaluate∫ 41∣∣
3 x− 6∣∣
dx.Set 3x− 6 =0;x=2; thus∣∣
3 x− 6∣∣
={
3 x−6ifx≥ 2
−(3x−6) ifx< 2.
Rewrite integral:
∫ 41∣
∣ 3 x− 6
∣
∣dx=∫ 21−(3x−6)dx+∫ 42(3x−6)dx=
[
− 3 x^2
2
+ 6 x] 21+
[
3 x^2
2
− 6 x] 42=(
−3(2)^2
2−6(2)
)
−(
−3(1)^2
2−6(1)
)+
(
3(4)^2
2−6(4)
)
−(
3(2)^2
2−6(2)
)=(− 6 +12)−
(
−3
2
+ 6
)
+(24−24)−(6−12)= 6 − 4
1
2
+ 0 + 6 =
15
2
.
Verify your result with a calculator.