(Solved): Show that the surface area of a sphere of radius a is still 4ra by using the following equation ( ...

Show that the surface area of a sphere of radius a is still 4ra² by using the following equation (with y=f(x) on the interval [a,b] revolved about the x-axis) to find the area of the surface generated by revolving the curve y = ?a²-x², -asxsa, about the x-axis. b b 2 dy S = 2xy 1+ -?2TY * dx = 2nf(x)/1+ (f(x)) ² dx dx First, find dy dx with y=?a²-x² X (a²-x²) Substitute the function, its derivative, and the given bounds into the provided formula. 3 X [ 2x (?a²-x²) | ? + (( ?²) 1+ dx Explain how this integral evaluates to 4ta². Select the correct choice below and fill in the answer box within your choice. OA. The integrand simplifies to which is not a constant. Integrating over the given integral results in 2?a²-2r(-a)², which simplifies to 4xa². B. The integrand simplifies to, which is a constant. Integrating over the given interval results in 2ra²-(-2ra²), which simplifies to 4xa². 112