1. Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)
Final Exam
1. Find the area bounded by the curve ๐ฆ = 3๐ฅ(๐ฅ โ 2)2
and the
x axis.
2. The area bounded by the hyperbola ๐ฅ2
โ ๐ฆ2
= ๐2
, the x-
axis, and the line x= 2a revolves Ox (x axis). Find the volume.
(Used circular disk)
3. The area bounded by the parabola ๐๐ฆ = ๐ฅ2
, the x- axis, the
line x= b is revolved about the y-axis. Find the volume
generated. (Used cylindrical shell method)