Question 871062
Q1 is correct but you can simplify a bit.
{{{1+(1/sqrt(x+7))^2=1+1/(x+7)}}}
{{{1+(1/sqrt(x+7))^2=(x+7)/(x+7)+1/(x+7)}}}
{{{1+(1/sqrt(x+7))^2=(x+8)/(x+7)}}}
so then,
{{{ds=sqrt((x+8)/(x+7))dx}}}
So then the area is,
{{{dA=2*pi*y*ds=2*pi*(2*sqrt(x+7))*sqrt((x+8)/(x+7))dx}}}
{{{dA=2*pi*y*ds=4*pi*sqrt(x+8)dx}}}