Question

19. Find area of the surface created by revolving r = 2 sinx from 0≤x≤π/2 around the line x = π/2​

Answer 1

Answer:

19. Find area of the surface created by revolving r = 2 sinx from 0≤x≤π/2 around the line x = π/2

answer of this question is 56.

Answer 2

Answer:

The requir

ed surface

re

a S

.A.

=∫ 0a 2πyds=

2π

∫ 0a y1+( dx

ddy ) 2dxHere y2

=

4ax⇒2yy ′ 4a⇒y= y2

aSo

1+( dxddy)

2=1+( y2a ) 2

=1+

y 24a 2=1+ 4ax4a 2=1+

=xx+ay 2=4ax⇒y= 4ax =2

ax∴ S.A. =∫ 0a2π(2ax

) xx+ads=4π a∫ 0a (x+a) 21d

x=4π a⎩⎪⎪⎨⎪⎪|23

[x+a] 23⎭⎪⎪⎬⎪⎪⎫0a= 38π a (2a) 23=

38πa

2(2 2

−1)sq.units.soluti

on