Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve y=sqrt(64-x^2), -1<=x<=1

Bergsteinj0 2022-09-27 Answered
Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve
y = 64 x 2 ,     1 x 1
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Answers (1)

Johnathon Mcmillan
Answered 2022-09-28 Author has 7 answers
6) For function y = f ( x ) ,       a x b
surface area obtained obtained by rotating the curve is given by,
s = 2 π a b f ( x ) 1 + d y d x 2 d x
y = f ( x ) = 64 x 2
f ( x ) = 2 x 2 64 x 2 = x 64 x 2 [ f ( x ) ] 2 = x 2 ( 64 x 2 ) 1 + ( f ( x ) ) 2 = 1 + x 2 64 x 2 = 64 64 x 2 f ( x ) 1 + ( d y d x ) 2 = 64 x 2 8 64 x 2 = 8
Answer:
2 π 1 1 8 d x = 32 π
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