Given $y=x,y=0,x=2$ and $x=7$. Calculate the volume6 about $x=1$.
I just need to get the concept right. Please tell me what mistake I did here.
The region looks like a trapezium right?
From $y=0$ to $y=2$, it's volume is a larger cylinder - smaller cylinder.
Which is $π(6^2)(2) - π(1^2)(2)$.
For $y=2$ to $y=7$,
I use the $A(y) = π(6)^2 - π(1+y)^2$ and then integrate $A(y)$ from $y=2$ to $y=7$ [outer radius - inner radius]
I can't seem to get the answer and I have a feeling my $A(y)$ is wrong. Can someone tell me which part of it is wrong?