Volumes with Cross Sections: Squares/Rectangles
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the volume for
s
(
x
)
=
3
x
s(x) = 3x
s
(
x
)
=
3
x
from
x
=
0
x=0
x
=
0
to
x
=
1
x=1
x
=
1
with square cross sections.
QUESTION
What is the formula for the volume of a solid with square cross sections?
QUESTION
Find the volume for
b
(
x
)
=
1
b(x) = 1
b
(
x
)
=
1
,
h
(
x
)
=
x
h(x) = x
h
(
x
)
=
x
, for
x
=
0
x=0
x
=
0
to
x
=
2
x=2
x
=
2
with rectangular cross sections.
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ANSWER
2
2
2
cubic units.
∫
0
2
1
⋅
x
d
x
=
[
x
2
2
]
0
2
=
2
\int_0^2 1 \cdot x dx = [\frac{x^2}{2}]_0^2 = 2
∫
0
2
1
⋅
x
d
x
=
[
2
x
2
]
0
2
=
2
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