Areas under simple curves and regions bounded by curves - One Line Questions
1.
What is the area of the region bounded by the curve y = sin(x), the x-axis, and the lines x = 0 and x = π? —
2
2.
Find the area of the region bounded by the curve y = x^3, the x-axis, and the lines x = -1 and x = 1. —
0
3.
Find the area of the region bounded by the curve y = x(x-1)(x-2) and the x-axis. —
1
4.
Calculate the area of the region bounded by the curve y = x^3 - x and the x-axis. —
1/2
5.
Calculate the area of the region bounded by the curve y = x^3 and the line y = x. —
1/2
6.
What is the area of the region bounded by the curve y = sec^2(x), the x-axis, and the lines x = 0 and x = π/4? —
1
7.
Find the area of the region bounded by the curve y = |x - 1| and the x-axis from x = 0 to x = 2. —
1
8.
What is the area of the region bounded by the curve y = 1/x, the x-axis, and the lines x = e and x = e^2? —
1
9.
What is the area of the region bounded by the curve y = 1/x^2, the x-axis, and the lines x = 1 and x = 2? —
1/2
10.
Find the area of the region bounded by the curves y = x^2 and y = 2x - x^2. —
1/3
11.
Find the area of the region bounded by the curve y = x^2 and the tangent line at x = 1. —
1/3
12.
Find the area of the region bounded by the curve y = x^2 and the line x = y^2. —
1/3
13.
Determine the area of the region bounded by the curve y = x^2 and its normal at x = 1. —
1/3
14.
Find the area of the region bounded by the curve y = x^2 and the line y = 4x - 3. —
1/3
15.
Calculate the area of the region bounded by the curve y = x^2 and the line y = x. —
1/6
16.
Find the area of the region bounded by the curve y = x^2 and the line y = 3x - 2. —
1/6
17.
Find the area of the region bounded by the curve y = x^2 and the line y = 5x - 4. —
1/6
18.
What is the area of the region bounded by the curve y = x^2 and the line y = 5x. —
125/6
19.
Find the area of the region bounded by the curve y = x^2 and the line y = 7x - 6. —
125/6
20.
Determine the area of the region bounded by the curve y = x^2 and the line y = 9 - x^2. —
128/3
21.
Determine the area of the region bounded by the curve y = x^2 - 4 and the x-axis. —
16/3
22.
What is the area of the region bounded by the curve y = x^2 and the line y = 4? —
32/3
23.
What is the area of the region bounded by the curve y = x^2 and the line y = 4x? —
32/3
24.
Determine the area of the region bounded by the curve y = x^2 and the line y = 6 - x^2. —
32/3
25.
Find the area of the region bounded by the curve y = |x| and the line y = 2. —
4
26.
Calculate the area of the region bounded by the curve y = x^4 and the line y = 1. —
4/5
27.
Calculate the area of the region bounded by the curve y = x^2 and the line y = 10 - x^2. —
256/3
28.
What is the area of the region bounded by the curve y = x^2, the x-axis, and the lines x = 1 and x = 3? —
26/3
29.
Calculate the area of the region enclosed by the parabola y^2 = 4ax and the line y = mx. —
4a^2 / (3m^2)
30.
Calculate the area of the region bounded by the curve y = x^2 and the line y = 8 - x^2. —
32/3
31.
What is the area of the region bounded by the curve y = x^2 and the line y = 7x. —
343/6
32.
Find the area of the region bounded by the curve y = x^2 and the line y = 9x - 8. —
343/6
33.
Determine the area of the region enclosed by the cardioid r = a(1 + cos(θ)). —
3πa^2/2
34.
Find the area of the region bounded by the curve y = x^2 and the line y = x + 2. —
27/4
35.
Calculate the area of the region bounded by the curve y = x^2 - 2x and the x-axis. —
2/3
36.
Find the area of the region bounded by the curve y = x^2 and the line y = 2 - x^2. —
8/3
37.
Calculate the area of the region bounded by the curve y = x^2 and the line y = 7 - x^2. —
64/3
38.
What is the area of the region bounded by the curve y = x^2 and the line y = 9x. —
729/6
39.
Find the area of the region bounded by the curve y = sqrt(x), the x-axis, and the line x = 4. —
16/3
40.
Determine the area of the region bounded by the curve y = x^2 and the line y = -x + 2. —
27/4
41.
What is the area of the region bounded by the curve y = x^2 and the line y = 3x. —
9/2
42.
What is the area of the region bounded by the hyperbola x^2/a^2 - y^2/b^2 = 1 and its latus rectum? —
2ab
43.
What is the area of the region bounded by the curve y = e^x, the x-axis, and the lines x = 0 and x = 1? —
e - 1
44.
Determine the area of the region bounded by the curve y = 1/x, the x-axis, and the lines x = 1 and x = 2. —
ln(2)
45.
What is the area of the region bounded by the curve y = tan(x), the x-axis, and the lines x = 0 and x = π/4? —
ln(2)
46.
What is the area of the region bounded by y = sin(x) and y = cos(x) between x = 0 and x = π/4? —
sqrt(2) - 1
47.
What is the area of the region bounded by the curve y = 1/(1+x^2) and the x-axis from x = -∞ to x = ∞? —
π
48.
Determine the area of the region bounded by the curve y = 1/sqrt(1-x^2) and the x-axis from x = 0 to x = 1. —
π/2
49.
What is the area of the region bounded by the curve y = sqrt(a^2 - x^2)? —
πa^2/2
50.
What is the area of the region bounded by the curve y = sqrt(a^2 - x^2) and the x-axis from x = 0 to x = a? —
πa^2/4