425
Answers
601–700
Answers and Explanations
3 16
23 16
2 3 16
3
2 3 16 4
2
4
4
2
0
4
3
0
4
−
(
)
(
) =
−
(
)
=
−
=
−
−
∫
∫
x
dx
x dx
x x
( )
( ( )
4
3
256 3
3
=
684.
96
Recall the definition of volume: Let S be a solid that lies between y = c and y = d. If A(y)
is the cross-sectional area of S in the plane P y that goes through y and is perpendicular
to the y-axis, where A is a continuous function, then the volume of S is
V
A y dx
c
d
= ∫ ( )
Here, you want to find an expression for A(y).
If you consider a cross-sectional slice that goes through a point (x, y) on the ellipse,
where x > 0, then one side of the square has length 2x. The area of the square is
( )
( )
2
4
4 1
4
36 9
3 6 9
2
2
2
2
x
x
y
y
A y
=
=
−
(
)
(
) = − =
Answers
601–700
Answers and Explanations
3 16
23 16
2 3 16
3
2 3 16 4
2
4
4
2
0
4
3
0
4
−
(
)
(
) =
−
(
)
=
−
=
−
−
∫
∫
x
dx
x dx
x x
( )
( ( )
4
3
256 3
3
=
684.
96
Recall the definition of volume: Let S be a solid that lies between y = c and y = d. If A(y)
is the cross-sectional area of S in the plane P y that goes through y and is perpendicular
to the y-axis, where A is a continuous function, then the volume of S is
V
A y dx
c
d
= ∫ ( )
Here, you want to find an expression for A(y).
If you consider a cross-sectional slice that goes through a point (x, y) on the ellipse,
where x > 0, then one side of the square has length 2x. The area of the square is
( )
( )
2
4
4 1
4
36 9
3 6 9
2
2
2
2
x
x
y
y
A y
=
=
−
(
)
(
) = − =