10.3 u Substitution Definite Integrals

10.3 u Substitution Definite Integrals
NOTES
Evaluate the indefinite integrals using u substitution.
Write your
questions here!
∫
1
√1 βˆ’ 4π‘₯ 2
𝑑π‘₯
Evaluate the indefinite integrals using u substitution.
∫
π‘₯
√π‘₯ + 1
𝑑π‘₯
DEFINITE INTEGRAL
2
∫ 𝑑 2 βˆšπ‘‘ 3 + 1𝑑𝑑
0
INVERSE TRIG
Evaluate the definite integrals using u substitution.
πœ‹
2
∫ cos(π‘₯)√sin(π‘₯) 𝑑π‘₯
0
𝑒
∫
0
SUMMARY:
Now,
summarize
your notes
here!
π‘₯2
π‘₯
𝑑π‘₯
+4
10.3 u Substitution Definite Integrals
Evaluate the definite integral.
1
1. ∫0
π‘₯
(π‘₯ 2 +1)3
𝑑π‘₯
πœ‹
2. ∫02 sin(2π‘₯) 𝑑π‘₯
3
3. ∫0 2π‘₯√3π‘₯ βˆ’ 5 𝑑π‘₯
10
4. ∫1 √5π‘₯ βˆ’ 1 𝑑π‘₯
PRACTICE
Evaluate the definite integral.
3
1
5. βˆ«βˆ’2 1+9𝑑 2 𝑑𝑑
5
6. ∫1 π‘₯√2π‘₯ βˆ’ 1𝑑π‘₯
6
7. ∫3 (π‘₯ 2 βˆ’ 2π‘₯)𝑑π‘₯
3
8. ∫1
8π‘₯
√1βˆ’16π‘₯ 2
𝑑π‘₯
Evaluate the definite integral.
√
πœ‹
4
9. ∫
πœ‹
√
8
βˆ’π‘₯csc 2 (2π‘₯ 2 )
𝑑π‘₯
cot(2π‘₯ 2 )
1
𝑦 2 + 2𝑦
10. ∫ 3
𝑑𝑦
3 + 3𝑦 2 + 4
βˆšπ‘¦
0
10.3 u Substitution Definite Integrals
MULTIPLE CHOICE
TEST PREP
l
3
14. An equivalent representation of the definite integral ∫1 2 cos(π‘₯ 2 )𝑑π‘₯ is
3
(A) ∫1 cos 𝑒 𝑑𝑒
9
(B) ∫1 cos 𝑒 𝑑𝑒
√3
(C) ∫1 cos 𝑒 𝑑𝑒
9
(D) ∫1 2βˆšπ‘’ cos 𝑒 𝑑𝑒
√3
(A) ∫1 2βˆšπ‘’ cos 𝑒 𝑑𝑒
5. B
12. C
9. C
13. E
14. B