Find volume of solid rotated about X axis Washer method

2.7taudi

1. The problem statement, all variables and given/known data

y=x^2+1
X in (0,1)

2. Relevant equations
formula needed
integral (PI [f(x)]^2 DX

in the F(x) just plug in the equation right?

3. The attempt at a solution
took anti deritive of the original problem and came out with

PI[1/3x^3+X]^2
my answer is 5.58

am i on the right track?

im confused on the squared part. Do i take the Anti deritive of the squared or only the thing inside the brackets?

Bohrok

Right, you plug f(x) into the formula, but that ^2 means you square f(x), so [f(x)]^2 = (x^2 + 1)^2. That's what you actually want to integrate.

2.7taudi

So how do i take the Anti deritive of that?

is it 1/3(x^2+1)^3*(1/3x^3+X)^2? im going blank lol should there be a ^2 at the end of that?

Bohrok

That wouldn't be the way to integrate it

Easiest way would probably be to multiply it out,
(x²+1)² = (x²+1)(x²+1) = ...
then integrate each term.

2.7taudi

Got it!

does this look right? excuse my chicken scratch handwriting.

Attached Thumbnails

 

Bohrok

Yep, that's it!