# Thread: Calc: Substitution Rule

1. ## Calc: Substitution Rule

the problem is Sin(x^3) x^2 dx

u = x^3
du = 3x^2

I noticed when my teacher was solving this out her final answer was -1/3 cos(x^3) + C

My question is where did the x^2 go and where did she pull out the 1/3 from?

2. $sin(x^3) x^2 dx$*
With the substitution you proposed you have
$u = x^3$
$\frac{du}{3} = x^2 dx$ And the expression becomes $sin(u) \frac{du}{3}$

3. I'm sorry but why is it dU/3? where did you get that?

4. $d(u) = du$

$d(u) = d(x^3) = 3x^2 dx = du$

If you divide the two last term by 3 you get

$x^2 dx = \frac{du}{3}$