Question

CALCULUS HELP! Find the volume of the solid obtained by rotating the region under the graph of the function

Answer 1

Answer:

14π

Step-by-step explanation:

Graph the region.  Rotated about the y-axis, the volume is a round, spherical shape.

Slice the volume into a vertical stack of discs.  The radius of each disc is x, the thickness of each disc is dy.  The volume of each disc is:

dV = π x² dy

dV = π (7 sin y) dy

dV = 7π sin y dy

The total volume is the sum of all the discs from y=0 to y=π.

V = ∫ dV

V = ∫₀ᵖⁱ 7π sin y dy

V = -7π cos y |₀ᵖⁱ

V = -7π (cos π − cos 0)

V = -7π (-1 − 1)

V = 14π