Question

Usar una esfera esfera formada al girar la gráfica de y-v/9_x2,0 alrededor del eje y Encuentre el área de la superficie de una 2, 57. x

Answer 1

Given:

y=(9-x²)^0.5

Find the derivative:

dy/dx= -0.5(9-x²)^-0.5(-2x)

dy/dx=x/ $\sqrt$ (9-x²)

1+(dy/dx)²=1+x²/(9-x²)

$\sqrt$ (1+(dy/dx)²)= $\sqrt$ 1+x²/(9-x²)= $\sqrt$ 9-x²+x²/(9-x²)=3/ $\sqrt$ (9-x²)

Surface area= $\int_{a}^{b}$ 2 $\pi$ f(x)[1+(dy/dx)²]^0.5.dx

Surface area= $\int_{0}^{2}$ 2 $\pi$ (9-x²)^0.53/(9-x²)^0.5.dx

A=6 $\pi$ $\int_{0}^{2}$ 1.dx

A=12 $\pi$ is the surface area of the solid