1
Trigonometric integrals and Trigonometric Substitutions- HW Problems
Evaluate the following integrals.
𝜋
1. ∫0 cos3 (𝑥 )𝑑𝑥
2
2. ∫[sin3 (𝑥 )][cos 2 (𝑥)]𝑑𝑥
3. ∫ cos4 (𝑥 )𝑑𝑥
4. ∫[tan2 (𝑥 )][sec 4 (𝑥)]𝑑𝑥
𝜋
5. ∫0 [tan3 (𝑥 )][sec 4 (𝑥)]𝑑𝑥
3
6. ∫ cot(𝜃 ) 𝑑𝜃
𝜋
7. ∫ cot 3 (𝑡)𝑑𝑡
𝜋
2
4
8. ∫[sin(𝑥 )][sin(2𝑥 )]𝑑𝑥
𝜋
9. ∫0 [tan2 (𝑥 )] 𝑑𝑥
4
1−tan2 (𝜃)
10. ∫ 𝑑𝜃
sec2 (𝜃)
1
11. ∫0 𝑥 2 √1 − 𝑥 2 𝑑𝑥
12. ∫ 𝑥 3 √𝑥 2 + 1𝑑𝑥
𝑑𝑥
13. ∫ √𝑥 2 +9
𝑑𝑡
14. ∫ 𝑡 2 √𝑡 2 −4
15. ∫ √4 − 𝑥 2 𝑑𝑥
Trigonometric integrals and Trigonometric Substitutions- HW Problems
Evaluate the following integrals.
𝜋
1. ∫0 cos3 (𝑥 )𝑑𝑥
2
2. ∫[sin3 (𝑥 )][cos 2 (𝑥)]𝑑𝑥
3. ∫ cos4 (𝑥 )𝑑𝑥
4. ∫[tan2 (𝑥 )][sec 4 (𝑥)]𝑑𝑥
𝜋
5. ∫0 [tan3 (𝑥 )][sec 4 (𝑥)]𝑑𝑥
3
6. ∫ cot(𝜃 ) 𝑑𝜃
𝜋
7. ∫ cot 3 (𝑡)𝑑𝑡
𝜋
2
4
8. ∫[sin(𝑥 )][sin(2𝑥 )]𝑑𝑥
𝜋
9. ∫0 [tan2 (𝑥 )] 𝑑𝑥
4
1−tan2 (𝜃)
10. ∫ 𝑑𝜃
sec2 (𝜃)
1
11. ∫0 𝑥 2 √1 − 𝑥 2 𝑑𝑥
12. ∫ 𝑥 3 √𝑥 2 + 1𝑑𝑥
𝑑𝑥
13. ∫ √𝑥 2 +9
𝑑𝑡
14. ∫ 𝑡 2 √𝑡 2 −4
15. ∫ √4 − 𝑥 2 𝑑𝑥
