/sci/ - Science & Math

[Anonymous No.3107979]

Hello /sci/, i need some help for my exam tomorrow.

Find the volume of the body which is limited by <div class="math">z_1=3x^2 +y^2+4y</div> and <div class="math">6x+2y+z_2=-3</div>

The answer sheet says <span class="math"> V=\frac{27\sqrt{3}\pi}{2}[/spoiler].

Here is my calculations:

For every point on the area which the body projects on the xy-plane, D, we have <span class="math">dz=z_2-z_1[/spoiler]. And the integral:
<div class="math">\int \int_D \left(\int_{3x^2 +y^2+4y}^{-3-6x-2y}dz\right)dxdy = \int \int_D (-3-6x-2y-3x^2 -y^2-4y)dxdy</div>
So now i start making variable changes to transform D into a circle, and i am remembering the Jacobian, but in the end i always get a newgative answer!

Help me

[Anonymous No.3108025]

bump

[Anonymous No.3108099]

bump

[Anonymous No.3108146]

bump!

[Anonymous No.3108181]

you again. Learn to play.

[Anonymous No.3108221]

bump

[Anonymous No.3108245]

Equal the z's and find the correct domain

The integral should have the form

<div class="math">\int_{a}^{b}\int_{f(x)}^{g(x)}\int_{h(x,y)}^{k(x,y)}</div>