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(a)
The function is and the interval is .
(i)
The surface area formula, for rotation about the - axis is .
Consider .
Differentiate the function with respect to .
Substitute corresponding values in .
The surface area :
The surface area of the curve obtained after rotation about - axis is .
(ii)
The surface area formula, for rotation about the - axis is .
Substitute corresponding values in .
The surface area :
The surface area of the curve obtained after rotation about - axis is .
(b)
From part (a) :
(i)
The surface area of the curve obtained after rotation about - axis is .
Using a calculator, the value of is .
From part (a) :
(ii)
The surface area of the curve obtained after rotation about - axis is .
Using a calculator, the value of is .
(a)
(i) .
(ii) .
(b)
(i) .
(ii) .
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