Volume (1 Viewer)

[prettypinkheart]

Find the volume of the solid of revolution formed, correct to 3 significant figures, if y=x^2 + 2 is rotated about the x-axis from x=0 to x=2.

I don't know what I'm doing wrong but I get 56.5.

The answer is supposed to be 78.7 units^3.

Hope someone can help me. Thanks if you can.

 

[tommykins]

回复: Volume

y = x^2+2
y^2 = (x^2+2)^2 = x^4 + 4x^2 + 4

v = pi int. x^4 + 4x^2 + 4 dx 2->0 = pi[x^5/5 + 4x^3/3 + 4x ] = 376pi/15 = 78.75 = 78.7 units^3 (3 sig fig)