1. ## Volume of solid

Dear Folks,

The base of the volume is the region between two parabolas.
Find the volume of the solid given that cross-sections perpendicular to the x-axis are squares.

2. ## Re: Volume of solid

Originally Posted by Simplictic
Dear Folks,

The base of the volume is the region between two parabolas.
Find the volume of the solid given that cross-sections perpendicular to the x-axis are squares.

$\displaystyle V = \int_a^b [f(x) - g(x)]^2 \, dx$

where $\displaystyle x = a$ and $\displaystyle x = b$ are the x-coordinates of the parabolas intersection points

$\displaystyle f(x)$ = upper parabola

$\displaystyle g(x)$ = lower parabola

in future, please place questions that involve integration in the calculus forum.

3. ## Re: Volume of solid

Originally Posted by skeeter
$\displaystyle V = \int_a^b [f(x) - g(x)]^2 \, dx$

where $\displaystyle x = a$ and $\displaystyle x = b$ are the x-coordinates of the parabolas intersection points

$\displaystyle f(x)$ = upper parabola

$\displaystyle g(x)$ = lower parabola

in future, please place questions that involve integration in the calculus forum.
Thanks skeeter,

If parabolas are $\displaystyle x = y^{2}$ and $\displaystyle x = 3 -y^{2}$, is it reasonable to make $\displaystyle y$ subject to have $\displaystyle y= f(x), y = g(x)$ or we need to use $\displaystyle x = f(y)$ in the formula for volume?

4. ## Re: Volume of solid

Originally Posted by Simplictic
Thanks skeeter,

If parabolas are $\displaystyle x = y^{2}$ and $\displaystyle x = 3 -y^{2}$, is it reasonable to make $\displaystyle y$ subject to have $\displaystyle y= f(x), y = g(x)$ or we need to use $\displaystyle x = f(y)$ in the formula for volume?
are the cross-sections still perpendicular to the x-axis?