# Substitution of a definite integral

1. Feb 3, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

Why does the 3x^2 disappear? Doesn't it play a role in the answer?

2. Feb 3, 2012

### jbunniii

It is explained in the first line of blue text:

$$du = 3x^2 dx$$

3. Feb 3, 2012

### bobsmith76

I think after you find the derivative of u, which is 3x^2, you divide that by 3x^2 which is 1, but I'm not sure

4. Feb 3, 2012

### jbunniii

No, it's a simple substitution.

$$u = x^3 + 1$$

Differentiating both sides with respect to x:

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

or equivalently

$$du = 3x^2 dx$$

Now substitute into the original integral. The $3x^2 dx$ turns into $du$, and $\sqrt{x^3 + 1}$ becomes $\sqrt{u}$. The endpoints of the integral also change accordingly.

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