Homework SourseFind the area of the surface obtained by rotating the curve
Find the area of the surface obtained by rotating the curve about the the y axis
y=1/4x^2-1/2lnx 1=<x=<2
explain the steps to reach to the correct answer which is 10pi/3
y=1/4x^2-1/2lnx 1=<x=<2
explain the steps to reach to the correct answer which is 10pi/3
Solution
dS = 2pi*y*v[1 + (y\')²] dx y = 1/4 x² - 1/2 lnx = 1/4*(x² - 2 lnx) y\' = 1/4*(2x - 2 * 1/x) = 1/2 * (x - 1/x) 1 + (y\')² = 1 + 1/4*(x - 1/x)² = 4/4 + 1/4*(x² - 2 + 1/x²) = = 1/4*(4 + x² - 2 +1/x²) = 1/4*(x² + 2 +1/x²) = 1/4*(x + 1/x)² So dS = 2pi*y*v[1/4*(x + 1/x)²] dx = = 2pi*1/4*(x² - 2 lnx)*1/2*(x + 1/x) dx = = pi/4 *(x² - 2 lnx)*(x + 1/x) dx S = pi/4*[2, 5] ? (x² - 2 lnx)*(x + 1/x) dx
