the area enclosed between the curve, the x axis and the ordiaate at x4. the volume of the solid obtained when the arca in (i) is rotated compleiely ahout the X-axis.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Answer Q2a

2.
(a)
The coordinates, (x), of points on the curve y = ffx) are given in the table below.
2.
3.
4
1.
4.
16
Use Simpson's rule to estimate
(i)
(ii)
the area enclosed between the curve, the x axis and the ordinate at x 4.
the volume of the solid obtained when the arca in (i) is retated completely ahout the
X- axis.
Oltaiu die Taylu scics capasion of y -a aloutx-An
Hence, or otherwise, show that if (xy). (x.,.). (x. ) arc successive point on the
()
curve y =x), such that Xn-X-=Xn+- X= h then
dy
Va * V. +
dx
(0)
dy
Ya * V+ 2h
de),
(i1)
(d'y
(ii)
(c)
Given that y satisfies the differential equation (x+1) = 2x - y,
dx
dy
usc the approximation y" y, +
dx
with A = 0.2 to find the value of y when.r- 0.4 given that y=1 when x= 0.
(Give your anawer to 3 signilicant ligurcs).
Transcribed Image Text:2. (a) The coordinates, (x), of points on the curve y = ffx) are given in the table below. 2. 3. 4 1. 4. 16 Use Simpson's rule to estimate (i) (ii) the area enclosed between the curve, the x axis and the ordinate at x 4. the volume of the solid obtained when the arca in (i) is retated completely ahout the X- axis. Oltaiu die Taylu scics capasion of y -a aloutx-An Hence, or otherwise, show that if (xy). (x.,.). (x. ) arc successive point on the () curve y =x), such that Xn-X-=Xn+- X= h then dy Va * V. + dx (0) dy Ya * V+ 2h de), (i1) (d'y (ii) (c) Given that y satisfies the differential equation (x+1) = 2x - y, dx dy usc the approximation y" y, + dx with A = 0.2 to find the value of y when.r- 0.4 given that y=1 when x= 0. (Give your anawer to 3 signilicant ligurcs).
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