Question

I am in the session 49, worked example. Question #1 confuses me. I know du=3xdx, but it suddenly becomes dx=1/3du! Where is x? Shouldn't it be dx=(1/3)xdu? Thank you in advance!

Answer 1

Here is a captured question and solution.

Answer 2

are you referring to
\[ \int_0^4 \sqrt{3x+4} \ dx \]
?
then let u =3x+4
take the derivative of both sides
\[ d u = d(3x+4) \\ du = 3 (d x) + d4 \\ du= 3\ dx \]

or, if you take the derivative with respect to x you would do
\[ \frac{d}{dx} u = \frac{d}{dx} \left( 3x+4\right) \\ \frac{du}{dx}= 3 \]
and if we separate the variables
\[ du = 3 \ dx\]

Answer 3

*** I know du=3xdx, ****
to get that you would have to start with
\[ u = \frac{3}{2} x^2 + C \]

Answer 4

The solution has a typo where they write " du = 3 x dx"