Answer :
Answer:
Step-by-step explanation:
the region is bounded by
. y = x + 1, y = 0, x = 0, x = 8;
and rotated about x axis.
The limits for x are from 0 to 8
The region is between x+1 and 0
Hence using washer method volume
= [tex]V=\pi\int\limits^8_0 {(x+1)^2-0^2} \, dx \\=\pi*\frac{(x+1)^3}{3}[/tex]
substitute limits
V=[tex]\frac{\pi}{3}9^3\\= 243\pi[/tex]
cubic units.
Answer:
The volume of the region is 763.02 cubic units.
Step-by-step explanation:
Given information:
Volume (V) of solid is obtained by the given curve about the line:
[tex]y=x+1[/tex]
At, [tex](y=0 ,x=0 , x=8)[/tex]
The region is between [tex]x+1[/tex] and [tex]0[/tex].
Hence, using Washer method ,
volume:
[tex]V=\pi \int\limits^0_8 {(x+1)^2}-0^2 \, dx[/tex]
[tex]V=\pi \times \frac{(x+1)^3}{3}[/tex]
On substituting limits , we get
[tex]V=243\pi[/tex] [tex]cubic[/tex] [tex]unit[/tex]
[tex]V=763.02[/tex] [tex]cubic[/tex] [tex]unit[/tex].
So, the volume of the region is 763.02 cubic units.
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