1
Antiderivatives- HW Problems
Find the following indefinite integrals
1. ∫(𝑥 − 4)𝑑𝑥
2. ∫(4𝑥 3 + 3𝑥 2 + 1)𝑑𝑥
3 1
3. ∫ ( √𝑥 2 + 𝑥) 𝑑𝑥
√
2𝑥4 −√𝑥
4. ∫ 𝑥3 𝑑𝑥
5. ∫(𝑦 + 2)(𝑦 3 − 𝑦)𝑑𝑦
6. ∫(𝑡 2 + 1)2 𝑑𝑡
7. ∫(2 cos(𝑥 ) − 3 sin(𝑥 ))𝑑𝑥
8. ∫(sec 2 (𝑥 ) − (csc(𝑥 ))(cot(𝑥 )))𝑑𝑥
9. ∫(3𝑥 2 + cos(3𝑥 ))𝑑𝑥
10. ∫[(sec(2𝑥 ))(tan(2𝑥 )) + csc 2 (3𝑥))]𝑑𝑥
Solve the following differential equations.
11. 𝑓 ′ (𝑥 ) = 2𝑥 + 3, 𝑓(0) = 2
12. 𝑓 ′ (𝑥 ) = 3𝑥 2 + sin(𝑥 ) , 𝑓(0) = 3
1
13. 𝑔′ (𝑡) = 3√𝑡 + , 𝑔(1) = 4
𝑡2
Antiderivatives- HW Problems
Find the following indefinite integrals
1. ∫(𝑥 − 4)𝑑𝑥
2. ∫(4𝑥 3 + 3𝑥 2 + 1)𝑑𝑥
3 1
3. ∫ ( √𝑥 2 + 𝑥) 𝑑𝑥
√
2𝑥4 −√𝑥
4. ∫ 𝑥3 𝑑𝑥
5. ∫(𝑦 + 2)(𝑦 3 − 𝑦)𝑑𝑦
6. ∫(𝑡 2 + 1)2 𝑑𝑡
7. ∫(2 cos(𝑥 ) − 3 sin(𝑥 ))𝑑𝑥
8. ∫(sec 2 (𝑥 ) − (csc(𝑥 ))(cot(𝑥 )))𝑑𝑥
9. ∫(3𝑥 2 + cos(3𝑥 ))𝑑𝑥
10. ∫[(sec(2𝑥 ))(tan(2𝑥 )) + csc 2 (3𝑥))]𝑑𝑥
Solve the following differential equations.
11. 𝑓 ′ (𝑥 ) = 2𝑥 + 3, 𝑓(0) = 2
12. 𝑓 ′ (𝑥 ) = 3𝑥 2 + sin(𝑥 ) , 𝑓(0) = 3
1
13. 𝑔′ (𝑡) = 3√𝑡 + , 𝑔(1) = 4
𝑡2
