1
Reversing the order of Integration- HW Problems
Change the order of integration and evaluate the integral both ways.
3 9
1. ∫0 ∫𝑦2 𝑑𝑥𝑑𝑦
4 ln(𝑥)
2. ∫1 ∫0 (3𝑥 2 𝑒 𝑦 )𝑑𝑦𝑑𝑥
2 2𝑥
3. ∫0 ∫𝑥 2 (3𝑦 2 )𝑑𝑦𝑑𝑥
Evaluate by changing the order of integration.
1 1
4. ∫0 ∫𝑦 (cos(𝑥 2 ))𝑑𝑥𝑑𝑦
1 1
5. ∫0 ∫𝑥 (𝑥√1 + 𝑦 3 )𝑑𝑦𝑑𝑥
2 2 2
6. ∫0 ∫𝑦 (e−x )𝑑𝑥𝑑𝑦
1 1
7. ∫0 ∫ 𝑦(sin(𝑥 3 ))𝑑𝑥𝑑𝑦
√
𝜋
1 4 5
8. ∫0 ∫tan−1 𝑥 (sec (𝑦))𝑑𝑦𝑑𝑥
Reversing the order of Integration- HW Problems
Change the order of integration and evaluate the integral both ways.
3 9
1. ∫0 ∫𝑦2 𝑑𝑥𝑑𝑦
4 ln(𝑥)
2. ∫1 ∫0 (3𝑥 2 𝑒 𝑦 )𝑑𝑦𝑑𝑥
2 2𝑥
3. ∫0 ∫𝑥 2 (3𝑦 2 )𝑑𝑦𝑑𝑥
Evaluate by changing the order of integration.
1 1
4. ∫0 ∫𝑦 (cos(𝑥 2 ))𝑑𝑥𝑑𝑦
1 1
5. ∫0 ∫𝑥 (𝑥√1 + 𝑦 3 )𝑑𝑦𝑑𝑥
2 2 2
6. ∫0 ∫𝑦 (e−x )𝑑𝑥𝑑𝑦
1 1
7. ∫0 ∫ 𝑦(sin(𝑥 3 ))𝑑𝑥𝑑𝑦
√
𝜋
1 4 5
8. ∫0 ∫tan−1 𝑥 (sec (𝑦))𝑑𝑦𝑑𝑥
