Deff. Intergration - find my mistake.

[the tree]

I'm trying to find: [math]\int_{0}^{12}12x^{\frac{1}{2}}-x^{\frac{3}{2}}\cdot dx[/math]

 

Which I thought was [math][12\times \frac{1}{1/2} x^{\frac{2}{3}} - \frac{1}{3/2} x^{\frac{5}{2}}]_0^{12}[/math]

 

Which I simplified to [math][24x^{\frac{2}{3}}-\frac{2}{3}x^{\frac{5}{2}}]_0^{12}[/math]

 

Which comes to aprox. 207.

 

But my textbook tells me that the awnser should be around 133.

 

Can anyone spot where I went wrong?

[timo]

The 2/3 in the exponent is wrong, didn´t check the rest.

[the tree]

Thanks, I'd been looking at that for far to long so there really was no chance of me spotting my blunder.

[5614]

Man I just spent like 10 mins doing this and it should take like 2... dunno what happened but you made mistakes all over the place, it confused me for a bit, until I started from scratch and got the right answer that way.

 

I've never done integrals on LaTeX, so let's see how it works out!

 

[math]y = 12x^{1/2} - x^{3/2}[/math]

 

[math]\int 12x^{1/2} \cdot dx = \frac{12x^{3/2}}{3/2} = 12x^{3/2} \times \frac{2}{3} = 8x^{3/2}[/math]

 

[math]\int x^{3/2} \cdot dx = \frac{x^{5/2}}{5/2} = x^{5/2} \times \frac{2}{5} = \frac{2x^{5/2}}{5}[/math]

 

Then you just combine the two:

 

[math]\int y \cdot dx = 8x^{3/2} - \frac{2x^{5/2}}{5}[/math]

 

Now we know that

 

[math]\int_{0}^{12} y \cdot dx \to [8x^{3/2} - \frac{2}{5}x^{5/2}]_0^{12}[/math]

 

You know how to finish it off now right?

 

Just stick in x=12 and get a value. Then stick in x=0 and subtract this from the original value you got for x=12.

 

It just happens for this question that when x=0 the whole thing =0 so you only really need to stick in x=12 and you get your answer.

 

Got it now?

 

btw, revising or are you just learning this?

[the tree]

Just learning. I wasn't tottally concentrating when I was noting the question in class, that'd explain the mess I made.

[5614]

Just finishing C2 then. Guessing you're not gonna have loadsa revision time in class.

 

I think this kind of integration is just a case of applying this:

 

[math]y = x^n[/math]

 

[math]\int x^n \cdot dx = \frac{x^{n+1}}{n+1}[/math]