Find volume of solid rotated about X axis Washer method

[2.7taudi]

Homework Statement

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

Homework Equations

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

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

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]

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.

So how do i take the Anti deritive of that?

is it 1/3(x^2+1)^3*(1/3x^3+X)^2? I am 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]

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.

Got it!

does this look right? excuse my chicken scratch handwriting.

 

[Bohrok]

Yep, that's it!