Question
Asked Oct 15, 2019

Solve parts these 2 parts of the question. Image attached.

The given curve is rotated about the y-axis. Find the area of the resulting surface.
y x3/2, 0 s x s 21
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The given curve is rotated about the y-axis. Find the area of the resulting surface. y x3/2, 0 s x s 21

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e3x, x z 0, is rotated about the x-axis, find the area of the resulting surface.
If the infinite curve y
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e3x, x z 0, is rotated about the x-axis, find the area of the resulting surface. If the infinite curve y

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Expert Answer

Step 1

a.

...
1
3
1
dy 1
dx
2
dy
dy
1
dx
6
dv
dx
21
Surface area
2
dx
21 xVx +4x
dx
6
2
0
21(2x+4-4)Vx+4x
dx
= 27
12
0
21
(2x+4)x+4x-4V+4xdx
21
(x2
x4x)x+4x
4 x+2)-4d
6
2
87521T 27
115 21
23 521
In
2
3
2
8
+
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1 3 1 dy 1 dx 2 dy dy 1 dx 6 dv dx 21 Surface area 2 dx 21 xVx +4x dx 6 2 0 21(2x+4-4)Vx+4x dx = 27 12 0 21 (2x+4)x+4x-4V+4xdx 21 (x2 x4x)x+4x 4 x+2)-4d 6 2 87521T 27 115 21 23 521 In 2 3 2 8 +

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