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Calculus 2 / Bc

250 Practice Problems

03:30
Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
The base of $S$ is the same base as in Exercise $42,$ but cross-sections perpendicular to the $x$ -axis are isosceles triangles
with height equal to the base.

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Nick J.
02:26
Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
The base of $S$ is the same base as in Exercise 40 , but cross-sections perpendicular to the $x$ -axis are squares.

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Nick J.
06:01
Essential Calculus Early Transcendentals

Each integral represents the volume of a solid. Describe the solid.
$$ \text { (a) }\pi \int_{0}^{\pi / 2} \cos ^{2} x d x \quad \text { (b) } \pi \int_{0}^{1}\left(y^{4}-y^{8}\right) d y$$

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Nick J.
01:19
Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
A pyramid with height $h$ and rectangular base with dimensions $b$ and 2$b$

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Rebecca P.
01:00
Essential Calculus Early Transcendentals

Find the volume of the described solid $S .$
A right circular cone with height $h$ and base radius $r$

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Rebecca P.
05:23
Essential Calculus Early Transcendentals

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
$$y=x^{2}, x^{2}+y^{2}=1, y \geqslant 0$$
(a) About the $x$ -axis (b) About the $y$ -axis

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Rebecca P.
02:58
Essential Calculus Early Transcendentals

A CAT scan produces equally spaced cross-sectional views
of a human organ that provide information about the organ
otherwise obtained only by surgery. Suppose that a CAT
scan of a human liver shows cross-scctions spaced 1.5 $\mathrm{cm}$
apart. The liver is 15 $\mathrm{cm}$ long and the cross-sectional areas,
in square centimeters, are $0,18,58,79,94,106,117,128,$
$63,39,$ and $0 .$ Use the Midpoint Rulc to estimate the volume of the liver.

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Rebecca P.
03:51
Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$y=x^{3}, y=\sqrt{x} ; \quad \text { about } y=1$$

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Rebecca P.
04:03
Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$y=x^{3}, y=\sqrt{x} ; \quad \text { about } x=1$$

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Rebecca P.
02:54
Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x=y^{2}, x=1 ; \quad \text { about } x=1$$

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Rebecca P.
04:10
Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x-y=1, y=x^{2}-4 x+3 ; \quad \text { about } y=3$$

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Rebecca P.
03:10
Essential Calculus Early Transcendentals

The region enclosed by the given curves is rotated about the specified line. Find the volume of the resulting solid.
$$x=2 y-y^{2}, x=0 ; \quad \text { about the } y-axis$$

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Rebecca P.
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