Question

the aera of the region bounded by the curves y=sinπx and x-axis is __________,where x ∈[0,2].

Answer 1

Answer:

Area = 2 areal units.  

Volume of the solid of revolution =  π^2/2  cubic units.

Step-by-step explanation:

Area =  ∫ydx = ∫sinxdx, between the limits  x=0 and x = π

= [−cosx], between the limits

=[−cosπ+cos0]

= [1 +  1 ]

=  2 areal units.

Volume =   π ∫y2dx =π∫sin2xdx, between the limits  x  =  0 and  x  =  π

= π/2∫(1−cos2x)dx, between the limits  x = 0 and x = π

= π/2 [ x − sin  2x/ 2 ] , between the limits

=π/2[(π−0)−(0−0)]

=π^2/2  cubic units

Hope It Might Helped You

Regards Vishal___

Answer 2

root 2/2 cubic units....

Missheartkiller ✨✌️