Calculus AB.
Some extra practice for sections 7.1 and 7.2.
1. Find the area of the region boundedby y=x+6,
y=x²,x=0, and x = 2.
2. Find the area of the region bounded by the curves y
=
x²andy
=
x+6.
3. Find the area of the region enclosed by x = y² andy =x-2.
4. Find the area of the region bounded by y= x²+1, y= x, x =-1, and x = 2.
1
and x = 4.
5. Find the area of the region enclosed by y =√x, y=--x,
4
6. Find the area bounded byx = y, x =
»x=ア» andy
=
2,
7. Find the area of the region bounded by x =-y and x =2- y².
8.
Find the volume of the solid that is obtained when the region under the curve y=√x
over the interval
[1,4] is revolved about the x-axis.
9. Derive the formula for the volume of a sphere of radius r. To do so, use the circle
x²+y² =r2
10. Find the volume of the solid generated when the region between the graphs of
and g(x)= x over the interval [0,2] is revolved about the x-axis.
f(x)=+x²
2
11. Find the volume of the solid generated when the region enclosed by
y=√x,y=2, and x
=
0 is revolved about the y-axis.
12. Find the volume generated when the region between y = x, y=
is revolved about the x-axis.
2-x2,and x= 0
13. Find the volume generated when the region bounded by the graphs of
y=3-2x, y
=
2,
y = 0, and x = 0 is revolved about the y-axis.