# Find volume using integrals

1. Jun 13, 2010

### kliker

find volume that is under z = 4x and over area D that is being blocked by y=x^2 y=0 and x=1

for y = 0 x must be 0 because y = x^2

so x will go from 0 to 1

y will go from 0 to x^2

but what about z? Will it go from 0 to 4x or should I say

z = 4x
y = x^2

that means y = z^2/16 => z = +/-4y

so z will be from -4y to 4y

here are the integrals

[PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP78419b3422a5ih9i1h4000014hgdh31a28gi7dh?MSPStoreType=image/gif&s=52&w=206&h=42 [Broken]

or

[PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP82019b343dd21edg47g00000i387ecif97gh4gf?MSPStoreType=image/gif&s=43&w=182&h=39 [Broken]

Last edited by a moderator: May 4, 2017
2. Jun 13, 2010

### HallsofIvy

Staff Emeritus
The first form is incorrect. y is not equal to $x^2$ throughout the region, only at the top boundary. z=4x on the entire region so the second integral is correct.

3. Jun 13, 2010

### kliker

thank you again i dont know what happened to the pictures, they suddenly dissapeared (wolfram alpha deleted them too)

thanks