HOW DO YOU SEE IT Use the graph to match the integral for the volume with the axis of
Chapter 7, Problem 54(choose chapter or problem)
HOW DO YOU SEE IT? Use the graph to match the integral for the volume with the axis of rotation.
(a) \(V=\pi \int_{0}^{b}\left(a^{2}-[f(y)]^{2}\right) d y\) (i) x-axis
(b) \(V=\pi \int_{0}^{a}\left(b^{2}-[b-f(x)]^{2}\right) d x\) (ii) y-axis
(c) \(V=\pi \int_{0}^{a}[f(x)]^{2} d x\) (iii) x = a
(d) \(V=\pi \int_{0}^{b}[a-f(y)]^{2} d y\) (iv) y =b
Text Transcription:
V=pi int_0^b (a^2 - [f(y)]^2) dy
V=pi int_0^a (b^2-[b-f(x)]^2) dx
V=pi int_0^a [f(x)]^2 dx
V=pi int_0^b [a-f(y)]^2 dy
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