Find the area of the surface obtained by rotating the curve...?

Question

y=sin(3x) about the x axis from x=0 to x=pi/3

Answer 1

For rotation about the x - axis, the surface area formula : .

For rotation about the y - axis, the surface area formula : .

The rotating curve y = sin(3x) about the x - axis from x = 0 to x = pi/3.

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Use the reduction formula : .

Multiply numerator and denominator of sec(u) by [ tan(u) + sec(u) ].

Answer 2

The curve is and the interval is .

Area of the surface  , since the region is being rotated about the x - axis.

Let,

Let,

Even integrand

Since, , .

The area of the surface obtained by rotating the curve about the x - axis from x = 0 to x = pi / 3 is .