Cartesian area rotated about y-axis

A question is this type if and only if it asks to find the volume or surface area when a region defined by a Cartesian or parametric curve is rotated about the y-axis, requiring integration with respect to y.

1 questions · Challenging +1.8

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CAIE FP1 2012 November Q6

7 marks Challenging +1.8

6 The curve \(C\) has parametric equations $$x = t ^ { 2 } , \quad y = \frac { 1 } { 4 } t ^ { 4 } - \ln t$$ for \(1 \leqslant t \leqslant 2\). Find the area of the surface generated when \(C\) is rotated through \(2 \pi\) radians about the \(y\)-axis.