Let f(x) = 9 - x^2. Let A be the area enclosed by the graph y = f(x) and the region y = 0.

Consider a thin strip of area of width delta(x) located at x.

Show with diagrams that the thin shell formed by rotating the small strip has volume:

delta(V) = 2[pi](63 - 9x - 7x^2 + x^3)delta(x)

Question

Let f(x) = 9 - x^2. Let A be the area enclosed by the graph y = f(x) and the region y >= 0.

Consider a thin strip of area of width delta(x) located at x.

Show with diagrams that the thin shell formed by rotating the small strip has volume:

delta(V) = 2[pi](63 - 9x - 7x^2 + x^3)delta(x)

amistre64 · Answer

have you drawn the picture yet?

amistre64 · Answer

radius = height of the strip, which is defined by f(x)
the width of the strip is just delta(x)

the volume of a cylindar of radius "r" and depth "delta(x)" is just

pi [f(x)]^2 delta(x)

anonymous · Answer

First draw the figure

anonymous · Answer

did u?