Question

1) 9 S r^3/(4+r^2)^(1/2)
steps: u=r^2 du=2rdr=du/2
9 S u/(4+u)^(1/2) du/2
(9/2) S u/(4+u)^(1/2) du
s=4+u and ds=du
(9/2) S -4+s/(s)^(1/2)
my question is why is s=4+u turn into negative4+s?

Answer 1

write the statement of question again ,iam not following

Answer 2

\[is \it 9 s=\frac{ r ^{3} }{ \left( 4+r ^{2} \right)^{\frac{ 1 }{ 2}}}\]

Answer 3

S is for integration

Answer 4

\[Let I=\int\limits \frac{ r ^{3} }{\sqrt{4+r ^{2}}}dr\]
\[put \sqrt{4+r ^{2}}=u,4+r ^{2}=u ^{2},r ^{2}=u ^{2}-4,2rdr=2udu,rdr=udu\]
\[I=\int\limits \frac{ r ^{2}r dr }{\sqrt{4+r ^{2}} }=\int\limits \frac{ \left( u ^{2}-4 \right)u du }{u }=\int\limits \left( u ^{2}-4 \right)du\]

Answer 5

now you can solve.