Odd QueStiOn.. (1 Viewer)

[+GriM ReApeR+]

Q. Use the trapezoidal rule with 4 subintervals to find an approximation to the volume of the solid formed by rotating the curve y=cosx about the x-axis from x=0 to x=pi/2.

Finding volume with trapezoidal rule?Is that possible?Help please?

Thanks

 

[Xayma]

A trapezium that is rotated will form a frustrum.

The volume of Frustrum is given by

V=h*pi/3 (R²+Rr+r²)

Where R is the radius of the lower base (ie the longer of the parallel sides)

and r is the radius of the upper base (ie the shorter of the parallel sides)

 

[redslert]

trapezoidal rule to find volume?

i have never done a question like that before....

Xayma eer what are you on about?
his doing a cos curve?

 

[+GriM ReApeR+]

Originally posted by Xayma
A trapezium that is rotated will form a frustrum.

The volume of Frustrum is given by

V=h*pi/3 (R²+Rr+r²)

Where R is the radius of the lower base (ie the longer of the parallel sides)

and r is the radius of the upper base (ie the shorter of the parallel sides)

ummm....hmmm......are we supposed to know this formula??

Originally posted by redslert
his doing a cos curve?

heeyyy..."his"?? u refering to me?? I'm not a guy...

 

[George W. Bush]

you can get an approximate expression for the area under the curve in terms of x.

 

[Heinz]

Originally posted by +GriM ReApeR+
Q. Use the trapezoidal rule with 4 subintervals to find an approximation to the volume of the solid formed by rotating the curve y=cosx about the x-axis from x=0 to x=pi/2.

Finding volume with trapezoidal rule?Is that possible?Help please?

Thanks

I did it.. but I dont agree with the answer I got. My "approximation" was equal to the exact area received through direct integration (pi²/4). Either I made a mistake (very likely) or I mustve used a hell of a lot of intervals

 

[+GriM ReApeR+]

hey...that was the answer in the textbook......smart smart!

 

[Heinz]

Originally posted by +GriM ReApeR+
hey...that was the answer in the textbook......smart smart!

hmm... well heres the working

 

[kpq_sniper017]

i've often done questions asking for approximations for volumes using simson's or trapezoidal.

all u have to do is approximate the integral using simpson's and multiply it by pi and then that's ur approximate for the volume. i think they do it in maths in focus in the challenge exercises.

 

[kpq_sniper017]

i did it on paper.....and i got an answer of pi²/4 which is approx. equal to 2.467u³

can somebody verify my answer?

 

[kpq_sniper017]

Originally posted by pcx_demolition017
i did it on paper.....and i got an answer of pi²/4 which is approx. equal to 2.467u³

can somebody verify my answer?

lol.....just realised heinz already it.

 

[Xayma]

Originally posted by redslert
Xayma eer what are you on about?
his doing a cos curve?

I know but he was doing the trapezoidal rule, and I forgot to just square it and then do the integral normally, so I fell back that a trapezoid that is rotated around a line will form a frustrum (ie a cone with the top bit cut off).

Heinz isnt that 5 subintervals?

 

[Heinz]

Originally posted by Xayma
I know but he was doing the trapezoidal rule, and I forgot to just square it and then do the integral normally, so I fell back that a trapezoid that is rotated around a line will form a frustrum (ie a cone with the top bit cut off).

Heinz isnt that 5 subintervals?

4 subintervals = 5 function values

 

[Xayma]

oh yeah, I though subinterval sounded wrong (I was thinking function values)