Answer to Question #253436 in Civil and Environmental Engineering for toto

Question

Find the volume generated by rotating the region bounded by line y=4 from x=1 to x=7, about the a. x-axis b. y-axis

Answer 1

Consider a region that is bounded by two curves 

$y=f(x)$

and

$y=g(x)$

between$x=a$ and $x=b$

$( f ( x ) , g ( x ) f(x),g(x)$ are continuous and non-negative on 

the interval $[a,b]$

And $f(x)\leq g(x)$ )

The volume of the solid formed by revolving the region about the x-axis is

$V=π a ∫ b ​ ([f(x)] 2 −[g(x)] 2 )dx$

We have three curves:$y=x, y^2=4x$ And x=1

The region that is bounded by them can be defined as a region that is bounded by$f(x)=2\sqrt {x}$

Answer: the volume is$\frac{5\pi}{3}.$