Disc Method: Revolving Around x/y Axes
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the volume of the solid obtained by revolving
y
=
x
2
y=x^2
y
=
x
2
from
x
=
0
x=0
x
=
0
to
x
=
2
x=2
x
=
2
around the x-axis.
QUESTION
Find the volume of the solid obtained by revolving
y
=
5
y=5
y
=
5
from
x
=
0
x=0
x
=
0
to
x
=
2
x=2
x
=
2
around the x-axis.
QUESTION
Find the volume of the solid obtained by revolving
y
=
1
x
y=\frac{1}{x}
y
=
x
1
from
x
=
1
x=1
x
=
1
to
x
=
2
x=2
x
=
2
around the x-axis.
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ANSWER
V
=
π
2
V = \frac{\pi}{2}
V
=
2
π
.
V
=
π
∫
1
2
1
x
2
d
x
=
π
[
−
1
x
]
1
2
=
π
2
V = \pi \int_1^2 \frac{1}{x^2} dx = \pi [-\frac{1}{x}]_1^2 = \frac{\pi}{2}
V
=
π
∫
1
2
x
2
1
d
x
=
π
[
−
x
1
]
1
2
=
2
π
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