2 unit integration (1 Viewer)

[otakuworld]

Find the shaded area is rotated around the y-axis. Find the volume of the solid formed.
This is the question. I don't understand how I keep getting this wrong! I used the formulas in the pic

 

[jazz519]

https://imgur.com/a/C2jMf
https://imgur.com/a/JHJR6
(if I didn't do any silly stuff should be right)

 

[otakuworld]

i'm not sure if this is right.I'm don't know if I even used the right formulas..on the sheet the answer says its 3π/2

 

[jazz519]

i'm not sure if this is right.I'm don't know if I even used the right formulas..on the sheet the answer says its 3π/2

n? we have values though. For ur equation can't be write because its around the y axis for the volume (so needs to be dy)

 

[otakuworld]

no sorry for some reason that Pi came out as an n

 

[jazz519]

no sorry for some reason that Pi came out as an n

oh right. I'll check my working again

 

[jazz519]

Oh lol my idiot brain changed a nine to a four and forgot the square (need to sleep rip)

So its v = pi (from 0 to 4) (4-y-y^2/9)dy
= pi (4y-y^2/2-y^3/27) (from 0 to 4)
= pi (16-8-64/27)
= pi (152/27)(which still isn't right lol)

 

[InteGrand]

no sorry for some reason that Pi came out as an n

π.

 

[jazz519]

Oh right I remember how to do this now gotta split the volumes (I'll post the pic in a sec)

 

[pikachu975]

Volume = pi [integral(0 to 3) (y^2 /9)dy + integral(3 to 4) (4-y)dy]
= pi [y^3 / 27](0 to 3) + [4y - y^2 /2](3 to 4)]
= pi [27/27 - 0 + 16 - 16/2 - 12 + 9/2]
= 3pi/2 u^3

 

[jazz519]

https://drive.google.com/open?id=1h621Xpp_RoT_euRGlTqpSdkfjKzcBEFG

 

[otakuworld]

I'll skip the area for now but thank you so much
I don't have to stay up

 

[otakuworld]

thank you!

 

[jazz519]

I'll skip the area for now but thank you so much
I don't have to stay up

Oh for the area do the same splitting thing from zero to three for the y=3x (which is a triangle), and three to four for the y= 4-xsqared