How is my integration wrong? X(

[Lo.Lee.Ta.]

My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x^3/2 - 2x² + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x^5/2/5/2 - 2(x³)/3 + 4x²/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

 

[Dick]

My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x^3/2 - 2x² + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x^5/2/5/2 - 2(x³)/3 + 4x²/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

Where did 4x^2/4 come from?

 

[Lo.Lee.Ta.]

Oh, sorry. I wrote down (4x^2)/2 on my paper but typed it wrong!

I meant (4x^2)/2

 

[Curious3141]

My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x^3/2 - 2x² + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x^5/2/5/2 - 2(x³)/3 + 4x²/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

448/15 = 29.8666666...

I'm guessing the system wants the exact answer, not a rounded off decimal.

 

[Dick]

Oh, sorry. I wrote down (4x^2)/2 on my paper but typed it wrong!

I meant (4x^2)/2

Ok. 448/15=29.8666... What do you think is wrong??

 

[Dick]

448/15 = 29.8666666...

I'm guessing the system wants the exact answer, not a rounded off decimal.

That's a good guess.

 

[Lo.Lee.Ta.]

Yeah, I guess it was the rounding thing! Man! :/

Thank you SO much for helping! Simple problem! UGH! =_=