Question Volumes (1 Viewer)

[kurt.physics]

I just have a question from a textbook that did not come with answers, its with volumes, its as follows

Find a formula for the area A(x) of the cross sections of the solids perpendicular to the x-axis.
Then find the Volume (if possible, i thought i did?)

The solid lies between planes perpendicular to the x-axis at x = 0 and x = 4. The cross-sections perpendicular to the x-axis between these planes run from the parabola y = -√x to the parabola y = √x

a) The cross-sections are circular disks with diameters in the xy-plane.

I have attached an image

Thanks, I just want to see if im right or not.

 

[Chinmoku03]

*Sigh, won't lemme post the symbols -.-;

I'll try hosting the image, brb

EDIT: Done, here's the link. Pretty sure it's right, but others are welcomed to check ^.^;

[img=http://img182.imageshack.us/img182/1739/areayn2.th.jpg]

 

[kurt.physics]

Hello, thanks for helping, but, i dont understand why you put

A = π4y²

i got the area

( I have a image attached to show why i think R(y) = √x )

A(y) = πR(y)²

where R(y) = √x

so then i got

∫A(y)dy = π ∫ R(y)²dy
= π ∫ (√x)²dy
= π (1/2 x²) (between x = 4 and x=0)
= 8π

Can you see whats wrong with my workout?

Thanks

 

[Chinmoku03]

Gah, I think my brain's decaying from taking too much rest after the trials x.x;

My bad, the radius of the circle is just y, not 2y, so the area is just πy²

So yeah, my answer should be divided by 4, making it 8π, which is your answer. Let's hope I didn't make another stupid mistake again x.x;

 

[kurt.physics]

<script type="text/javascript"> vbmenu_register("postmenu_3049384", true);</script>Thanks for your help, i will continue to study this 4U volumes. I dont know why you, mchappypants, are finding volumes hard, I think volumes is the most easiest topic out of four unit equil with integration, the hardest, i reckon is, well i cant say,wouldnt know.

Thanks everyone for helping

Two thumbs up

 

[kurt.physics]

Holly crap, is that all complex numbers is, thats ea-zay. And i would have to agree with you on volumes. The logic is easy, untill it gets really dirty! I must be having a bad maths week

I'll admit, this is VERY stupid of me. There was a question

∫ √(5x + 2)⁵ dx

I had previously got

√(5x + 2)⁷ / 17.5 + C

God, I should slap myself in the face, lol. But now i get (like everyone else)

2√(5x + 2)⁷ / 35 + C

Gosh, im losing my brain!!! HELP!!!


EDIT: The answer of 2√(5x + 2)⁷ / 35 + C is write according to the text book

 

[SoulSearcher]

1/17.5 = 1/(35/2) = 2/35?