Find the area of the surface generaled by revolving the

nemired9

nemired9

Answered question

2021-12-11

Find the area of the surface generaled by revolving the curve x=y35, 0y3 about the y-axis.

Answer & Explanation

Elois Puryear

Elois Puryear

Beginner2021-12-12Added 30 answers

Step 1
The curve x=g(y), cyd is revolved about the x-axis, then area of the surface is
A=2πcdg(y)1+[g(y)]2dy
Step 2
Now differentiate g(y)=y32, with resprct to y, we get
g(y)=3y25
Step 3
Now substitute the value of g(y) and g(y) in above formula, we get
A=2π03y351+(3y25)2dy
Step 4
Simplify the above integral, we get
A=2π03y351+(3y25)2dy
A=2π503y31+9y425dy
Put 1+9y425=uy3dy=2536dy
When y=0, u=1 and when y=3, u=75425
So, A=2π52536174525udu
A=5π18[u3232]175425
A=5π18[(75425)321]
A=5π27[165.631]
A=30.49π

enlacamig

enlacamig

Beginner2021-12-13Added 30 answers

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