HELP! integral using polar coordinates

[mknoow]

A pudding is made in a butterfly shape by generating r=e^cosθ-2cos 4θ about the polar axis and make it 2cm height?
So, to get a butterfly shape, two r is used, r1=e^cosθ-2cos 4θ and r2=-e^cosθ+2cos 4θ,
but i can't seem to integrate this when i reach integrate by theta, am i doing it wrong?

 

[Steven G]

I am not sure why there is a question mark at the end of the 1st line. Also, what is a pudding in this problem?

Can you please post the exact question? A picture of the problem would be best.

Also if you want help you need to follow the posting guidelines by showing us your work so we know what type of help you need. Thanks!

 

[mknoow]

okay thank you for being patient with me, here is the question,
Your bakery shop wants to manufacture a strawberry pudding in the butterfly shape. You designing a shape for strawberry pudding by generating r=e^cosθ-2cos 4θ about the polar axis and make it 2cm height. You decide to put out a deluxe version by packing 5 strawberry puddings in a box. You need to know how much mixture of strawberry pudding to have on hand for a production run of 800 boxes. Sketch graph of r.

 

[mknoow]

so far ive tried this but the e^cos(theta) is giving me troubles.

 

[LCKurtz]

I have made a couple of assumptions about what you really want and plugged it into a Maple worksheet. It calculates the volume of a single cake 2cm high with the shape given (which is my best guess at what you want):


Edit, added: I was thinking this was a real world problem, not a homework problem. If I'm wrong, c'est la vie.

 

[mknoow]

I have made a couple of assumptions about what you really want and plugged it into a Maple worksheet. It calculates the volume of a single cake 2cm high with the shape given (which is my best guess at what you want):

View attachment 19798
Edit, added: I was thinking this was a real world problem, not a homework problem. If I'm wrong, c'est la vie.

Oh my, the butterfly u got is pretty much better than mine,
I got this by using r and and inverse r to get a somewhat butterfly shape, i will take a look on your graph, but may i also know how do i find the volume? Because from what i know i cant seem to be able to integrate r, it gives me indefinite.

 

[mknoow]

I have made a couple of assumptions about what you really want and plugged it into a Maple worksheet. It calculates the volume of a single cake 2cm high with the shape given (which is my best guess at what you want):

View attachment 19798
Edit, added: I was thinking this was a real world problem, not a homework problem. If I'm wrong, c'est la vie.

But tbh this is amazing, i wasnt able to get any coordinates, and actually got stucked here

 

[LCKurtz]

Your graphs don't look like butterflies because you apparently didn't plot them in polar coordinates. You don't need a triple integral to do volume when you have a constant height. Just take the area of the base times the height. So you really have just an area problem. As shown in my worksheet, the area formula in polar coordinates is [MATH]A=\frac 1 2 \int_{\theta_1}^{\theta_2} r^2~d\theta[/MATH]. You don't get a simple integral you can evaluate by hand. I let Maple give a numerical answer.

 

[mknoow]

Your graphs don't look like butterflies because you apparently didn't plot them in polar coordinates. You don't need a triple integral to do volume when you have a constant height. Just take the area of the base times the height. So you really have just an area problem. As shown in my worksheet, the area formula in polar coordinates is [MATH]A=\frac 1 2 \int_{\theta_1}^{\theta_2} r^2~d\theta[/MATH]. You don't get a simple integral you can evaluate by hand. I let Maple give a numerical answer.

ohh i see, thank you so much for your time! I'm happy to be able to solve this now DD