Using Integration to calculate volume

This time we will started to learn how to use integration to calculate volume

Now we will started with a function we will started to calculate if the function rotating 360 degrees on the x axis, and it will never leave the axis, and then it will formed a 3 dimensional axis. we will called this solid of revolution, because we obtain it by revolving a region about a line.

if we say the function is $f(x)={\sqrt {x}}$ $\int _{0}^{1}A(x)dx$

so the radius of a circle will be r and $r={\sqrt {x}}$

and we can think it as the volume is made of many disk and it will formed this volume.

So the area of the disk will be like this $A=\pi r^{2}$

$r={\sqrt {x}}$

$r^{2}=x$

so

$A=\pi {({\sqrt {x}})}^{2}$

$A(x)=\pi x$

so what we will get this

$\int _{0}^{1}\pi xdx$

so $\pi$ is a constant so we can pull it out

$\pi \int _{0}^{1}xdx$