427
Answers
601–700
Answers and Explanations
Because the base of the solid varies for y over the interval [0, 4], the limits of integration
are 0 and 4. Therefore, the integral to find the volume is
1
2
2 2
2
1
8
2
1
2
1
24
2 4
2
0
4
2
0
4
2
3
0
4
−
=
− +
(
)
=
−
+
(
)
=
−
∫
∫
y dy
y
y dy
y
y
y
( ) 1 1
2
4
1
24
4
8
3
2
3
( )
( )
+
=
686.
16
Recall the definition of volume: Let S be a solid that lies between x = a and x = b. If A(x)
is the cross-sectional area of S in the plane P x that goes through x and is perpendicular
to the x-axis, where A is a continuous function, then the volume of S is
V
A x dx
a
b
= ∫ ( )
Here, you want to find an expression for A(x).
Answers
601–700
Answers and Explanations
Because the base of the solid varies for y over the interval [0, 4], the limits of integration
are 0 and 4. Therefore, the integral to find the volume is
1
2
2 2
2
1
8
2
1
2
1
24
2 4
2
0
4
2
0
4
2
3
0
4
−
=
− +
(
)
=
−
+
(
)
=
−
∫
∫
y dy
y
y dy
y
y
y
( ) 1 1
2
4
1
24
4
8
3
2
3
( )
( )
+
=
686.
16
Recall the definition of volume: Let S be a solid that lies between x = a and x = b. If A(x)
is the cross-sectional area of S in the plane P x that goes through x and is perpendicular
to the x-axis, where A is a continuous function, then the volume of S is
V
A x dx
a
b
= ∫ ( )
Here, you want to find an expression for A(x).