Thread: u-subsitution.

1. u-subsitution.

I understand how to do it's just I don't understand what a certain part of my homewor kmeans.
Using the method of u-substitution,

$\displaystyle $$\displaystyle \int_{2}^{4} (5 x - 7)^{4} \, dx = \int_{a}^{b} f(u) \, du$$$

where

$\displaystyle u = 5x-7$ (enter a function of x)
$\displaystyle du = 5$ dx (enter a function of x)
$\displaystyle a =2$ (enter a number)
$\displaystyle b =4$ (enter a number)
$\displaystyle f(u) =?$ (enter a function of u).

The value of the original integral is .
What does f(u) mean? I plug in u for the values of x?

2. Zanderist,

When you have $\displaystyle f(x) = (5x-7)^4$ its clever to choose $\displaystyle 5x-7 = u$, because you are left with $\displaystyle (u)^4$, so $\displaystyle f(u) = u^4$ and $\displaystyle \int u^4 du = \frac{u^5}{5}$, which is "more simple" than the integral with respect of x.

3. Recheck your upper and lower bounds.
Originally Posted by Zanderist
I understand how to do it's just I don't understand what a certain part of my homewor kmeans.
What does f(u) mean? I plug in u for the values of x?
$\displaystyle f(u)$ is the new integrand, the function which you have obtained in terms of $\displaystyle u$ after the substitution.
I plug in u for the values of x?
No, the whole point of the substitution was to get a new function that's easier to integrate.