$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute the limits 1 ≤ y ≤ 9

\

$\"\"$

\

Let 2y-3 = u

\

2dy = du

\

dy = du/2

\

And 2y-3 = u ⇒ y = (u+3)/2

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Let u² = k

\

2udu = dk

\

du = dk/2u

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Let 13k-81 = p

\

13dk = dp

\

dk = dp/13

\

And 13k-81 = p ⇒ k = (p+81)/13

\

$\"\"$

\

$\"\"$

\

Let √p = q

\

1/2√pdp = dq

\

dp = dq2√p

\

dp = 2qdq

\

And √p = q ⇒ p = q²

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

q = √p

\

q = √(13k-81)

\

q = √(13u²-81)

\

q = √(13(2y-3)²-81)

\

$\"\"$

\

Substitute intervals from 9 to 1

\

$\"\"$

\

$\"\"$

\

$\"\"$