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Area Between Curves- HW Problems
Find the area of the region bounded by the functions given. Start by
sketching the region.
1. 𝑦 = 4 − 𝑥2, 𝑦 = 𝑥2 − 4
2. 𝑦 = −𝑥 2 + 5𝑥 + 1, 𝑦 = 𝑥 + 1.
3. 𝑦 = 𝑥, 𝑦 = 4 − 𝑥, 𝑦 = 0.
4. 𝑦 = √4𝑥 + 2, 𝑦 =𝑥+2
5. 𝑦 = (𝑥 − 1)2 , 𝑦 = (𝑥 − 5)2 , 𝑥 = 1, 𝑥 = 5
𝜋
6. 𝑦 = sin(𝑥 ) , 𝑦 = cos(𝑥 ) , 𝑦 = 0, 0 ≤ 𝑥 ≤
2
7. 𝑥 = 𝑦2, 𝑥 =𝑦+2
8. 𝑦 = 𝑥 − 1, 𝑦 2 = 2𝑥 + 6
9. 𝑥 = 3𝑦 2 , 𝑥 = −𝑦 2 + 12𝑦 − 5
10. 𝑥 = 12 − 𝑦 2 , 𝑥 = 𝑦2 − 6 .
Area Between Curves- HW Problems
Find the area of the region bounded by the functions given. Start by
sketching the region.
1. 𝑦 = 4 − 𝑥2, 𝑦 = 𝑥2 − 4
2. 𝑦 = −𝑥 2 + 5𝑥 + 1, 𝑦 = 𝑥 + 1.
3. 𝑦 = 𝑥, 𝑦 = 4 − 𝑥, 𝑦 = 0.
4. 𝑦 = √4𝑥 + 2, 𝑦 =𝑥+2
5. 𝑦 = (𝑥 − 1)2 , 𝑦 = (𝑥 − 5)2 , 𝑥 = 1, 𝑥 = 5
𝜋
6. 𝑦 = sin(𝑥 ) , 𝑦 = cos(𝑥 ) , 𝑦 = 0, 0 ≤ 𝑥 ≤
2
7. 𝑥 = 𝑦2, 𝑥 =𝑦+2
8. 𝑦 = 𝑥 − 1, 𝑦 2 = 2𝑥 + 6
9. 𝑥 = 3𝑦 2 , 𝑥 = −𝑦 2 + 12𝑦 − 5
10. 𝑥 = 12 − 𝑦 2 , 𝑥 = 𝑦2 − 6 .
