PRACTICE PROBLEMS
Area Under a Curve
1.
Find the area of the region bounded by the curve 𝑦 = 𝑥 2 from 𝑥 = 0 to 𝑥 = 3.
2. Calculate the area bounded by the region by the line 𝑦 = 𝑥, from 𝑥 = -4 to 𝑥 = 4.
3. Calculate the area bounded by the region by the line 𝑦 = 8 − 2𝑥, the x-axis, and the y-axis.
4. Find the area of the region bounded by the curve 𝑦 = −𝑥 2 + 6𝑥 − 8.
5. Find the area of the region bounded by the curve 𝑦 = 3𝑥 − 𝑥 2 from 𝑥 = −2 to 𝑥 = 3.
6. Find the area of the region bounded by the curve 𝑦 = 𝑥 2 + 1 and 𝑦 = 4.
7. Compute the area of the region enclosed by the graphs of the equations 𝑥 = 𝑦 2 and 𝑥 = 4.
Area Between Two Curves
8. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 2 and 𝑦 = −𝑥 2 +
4𝑥 + 6.
9. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 2 and 𝑦 = 𝑥.
10. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 3 and 𝑦 = 4𝑥.
11. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 2 − 2𝑥 + 2 and
𝑦 = 2𝑥 + 2.
12. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 2 and 𝑥 = 𝑦 2 .
13. Compute the area of the region enclosed by the graphs of the equations 𝑦 = 𝑥 2 − 4𝑥 and 𝑦 =
6 − 3𝑥.
14. Compute the area of the region enclosed by the graphs of the equations 𝑥 = 𝑦 + 3 and 𝑥 =
𝑦 2 − 𝑦.
15. Compute the area of the region enclosed by the graphs of the equations 𝑥 = 𝑦 3 and 𝑥 = 𝑦 2 +
2𝑦.
16. Compute the area of the region enclosed by the graphs of the equations 𝑥 = 1 − 𝑦 2 and 𝑥 =
𝑦 2 − 1.
17. Compute the area of the region enclosed by the graphs of the equations 𝑥 = 3𝑦 − 2 and 𝑥 =
2𝑦 2 − 4.