Question
Find the exact area of the surface obtained by rotating the curve about the x-axis.
y=((x^3)/4)+(1/3X), 1/2≤X≤1
y=((x^3)/4)+(1/3X), 1/2≤X≤1
Answers
Steve
just plug and chug. The surface can be thought of as a stack of thin rings.
A = ∫2πr ds
where r=y and ds=√(1+y'^2) dx
so,
y' = (9x^4-4)/(12x^2)
A = 2π∫[1/2,1] (x^3/4+1/(3x))*((9x^4+4)/(12x^2)) dx = 1981π/3072
A = ∫2πr ds
where r=y and ds=√(1+y'^2) dx
so,
y' = (9x^4-4)/(12x^2)
A = 2π∫[1/2,1] (x^3/4+1/(3x))*((9x^4+4)/(12x^2)) dx = 1981π/3072