1 point
When we rotate a little rectangle with height \(f(x)\) around the \(x\)-axis we obtain a slice. If we cut the interval \([a, b]\) and we rotate each rectangle, the resulting solid would look
like the following one.
Assume that the volume of each slice is \(\pi (f(x_i))^2\) where \(x_i\) is a point in the interval where we are making the cut.
What is the volume of the resulting solid when the number of slices approaches to infinity?
$\int_a^b \pi f(x) \, dx$
$\Box\) length \cdot width \cdot height
$\int_a^b \pi (f(x))^2 \, dx$
$\int_a^b \pi (f(x))^2 \, dx$
$\Box\) \(\pi r^2\)
$\int_a^b \pi f^2(x) \, dx$
Clear my selection
