anonymous
  • anonymous
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!
OCW Scholar - Single Variable Calculus
chestercat
  • chestercat
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anonymous
  • anonymous
Here is a captured question and solution.
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phi
  • phi
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 \[ du = 3 \ dx\]
phi
  • phi
*** I know du=3xdx, **** to get that you would have to start with \[ u = \frac{3}{2} x^2 + C \]

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

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