Solution:
The curve y = x2 from x = 0 and x = 1 about the y axis
We know that x = 0 to x = 1 , which is analogous from y = 0 to y = 1.
Area of the surface is
A=2×π∫abg(y)1+(g′(y)2)dy
g(y)=y
g′(y)=(2×y)1
A=2×π∫01y1+((2×y)1)2dy
⇒A=2×π∫01y(1+4y1)dy
⇒A=2×π∫01y+(41)dy
Let,
u=y+41
⇒du=dy
y=0,u=41
y=1,u=45
⇒A=2×π∫4145u21du
⇒A=2×π[32(u23)]∣4145
⇒A=34×π[(45)23−(41)23]
⇒A=5.33sq.unit
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