Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.5, Problem 32PS
To determine
To find: the volume
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1. у%3D х3 — 2х2 + 3х — 5
y =
3 – 2x² + 3x – 5
dy
- Зx2 —
dx
4x + 3
Find the area enclosed by the line
y = x − 3
and the parabola
y2 = 2x + 18.
SOLUTION By solving the two equations we find that the points of intersection are
, −4
and
, 6
.
We solve the equation of the parabola for x and notice from the figure that the left and right boundary curves are
xL =
1
2
y2 − 9 and xR = y + 3.
We must integrate between the appropriate y-values,
y = −4
and
y = 6.
Thus
A
=
6
(xR − xL) dy
−4
=
6
(y + 3) −
dy
−4
=
6
dy
−4
=
6
−4
=
+ 18 + 72 −
+ 8 − 48
=
.
1.
5
10-4x
5-2z-y
6z2 dz dy da
0.
Chapter 12 Solutions
Calculus
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
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