1
The Fundamental Theorem of Calculus- HW Problems
Evaluate the definite integrals with part 2 of the Fundamental Theorem
of Calculus
2
1. ∫0 2𝑥𝑑𝑥
3
2. ∫1 (3𝑥 2 + 1)𝑑𝑥
1
3. ∫0 (2𝑡 + √𝑡)𝑑𝑡
4 4
4. ∫1 √𝑥 𝑑𝑥
1 1
5. ∫0 𝑥(√𝑥 − √𝑥 3 )𝑑𝑥
𝜋
6. ∫0 cos(𝑥 ) 𝑑𝑥
2
𝜋
7. ∫ sec 2 (𝜃 ) 𝑑𝜃
4
𝜋
−4
𝜋
3
8. ∫ (sec(𝑥 ))(tan(𝑥 ))𝑑𝑥
𝜋
−3
4 𝑥 2 −𝑥
9. ∫1 ( √𝑥 )𝑑𝑥
𝜋
4 sin2 (𝑥)+cos2 (𝑥)
10. ∫𝜋 ( )𝑑𝑥
sin2 (𝑥 )
6
The Fundamental Theorem of Calculus- HW Problems
Evaluate the definite integrals with part 2 of the Fundamental Theorem
of Calculus
2
1. ∫0 2𝑥𝑑𝑥
3
2. ∫1 (3𝑥 2 + 1)𝑑𝑥
1
3. ∫0 (2𝑡 + √𝑡)𝑑𝑡
4 4
4. ∫1 √𝑥 𝑑𝑥
1 1
5. ∫0 𝑥(√𝑥 − √𝑥 3 )𝑑𝑥
𝜋
6. ∫0 cos(𝑥 ) 𝑑𝑥
2
𝜋
7. ∫ sec 2 (𝜃 ) 𝑑𝜃
4
𝜋
−4
𝜋
3
8. ∫ (sec(𝑥 ))(tan(𝑥 ))𝑑𝑥
𝜋
−3
4 𝑥 2 −𝑥
9. ∫1 ( √𝑥 )𝑑𝑥
𝜋
4 sin2 (𝑥)+cos2 (𝑥)
10. ∫𝜋 ( )𝑑𝑥
sin2 (𝑥 )
6
