# Integration by parts mistake

1. Feb 9, 2012

### bobsmith76

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

In this video from which there is a screen shot above the author went from x/2 to 2x and all he said was half is two quarters. right a half is two quarters it is not 2. I just want to make sure that he made a mistake because i've been seeing some real bizarre things in the solution manual re integration by parts that i do not understand. everything else in the above simplification i understand except how

x/2 cos becomes 2x cos

2. Feb 9, 2012

### Sourabh N

Notice the $\frac{1}{4}$ outside the bracket? $\frac{x}{2} cos$ becomes $\frac{1}{4}(2x*cos$

3. Feb 9, 2012

### bobsmith76

I would think 1/4 * x/2 would make x/8.

4. Feb 9, 2012

### Sourabh N

Indeed. Look at what I wrote, again. Let me rephrase it: $\frac{x}{2} cos$ = $\frac{1}{4}(2x*cos$

5. Feb 9, 2012

### bobsmith76

are you saying somehow they got (x/2)/(1/4). That would make 1/2 * 4, but I don't see how that move is justified.

6. Feb 9, 2012

### Sourabh N

Nope! In the first step they have $\frac{x}{2}$. right?
In the second step, they have $\frac{1}{4}2x$. right?
Now, $\frac{x}{2}$ = $\frac{1}{4}2x$. right?

7. Feb 9, 2012

### bobsmith76

Ok, I got it. Thanks. Sorry for being so hard-headed

8. Feb 9, 2012

### Sourabh N

Happens You're welcome!