Question

7. When dy/dx = (x -6)1/2, what does y equal?

Answer 1

The answer is below
$\frac{dy}{dx} = \frac{1}{2} (x - 6)$
multiply both sides by dx

$dy = \frac{1}{2} (x - 6)dx$
integrate both sides of the diffrential

$integral \: dy = integral \: \frac{1}{2} (x - 6)dx$
simplify and integrate to get y alone don't forget to tack on c with your indefinite integral

$y = \frac{x {}^{2} }{4} - 3x + c$