# Having trouble simplifying this integral

• Oct 1st 2010, 11:42 AM
solidstatemath
Having trouble simplifying this integral
So I have to evluate the integral and simplify it. I'm stuck near the end after applying F(b) - F(a) and can't simplify it further.
• Oct 1st 2010, 12:59 PM
pickslides
$\displaystyle \displaystyle \int (y^2-\sin y)~dy =\frac{y^3}{3}+\cos y \neq \frac{y^3}{3}-\cos y$
• Oct 1st 2010, 01:06 PM
solidstatemath
Wait so it's + cos y and not - cos y? But to get -sin y it has to be -cos y.
• Oct 1st 2010, 01:10 PM
pickslides
Quote:

Originally Posted by solidstatemath
Wait so it's + cos y and not - cos y? But to get -sin y it has to be -cos y.

I understand it as

$\displaystyle \displaystyle \frac{d}{dy}\sin y =\cos y$

and

$\displaystyle \displaystyle \frac{d}{dy}\cos y =-\sin y$

therefore

$\displaystyle \displaystyle \int-\sin y ~dy = \cos y +C$
• Oct 3rd 2010, 12:09 PM
solidstatemath
I'm having trouble simplifying this.

I got:

[(4pi/5)^3 / 3] - [COSpi4/5] - [(-4pi/5)^3 / 3] - [-COS(-4pi/5)]

I think the COS term will cancel out and then we get 2[(4pi/5)^3 / 3] as the answer.

Things I am not sure about: the signs. I'm not sure about:

- [-COS(-4pi/5)] *** does this become positive? What about the -4pi/5?
• Oct 3rd 2010, 12:16 PM
solidstatemath
Okay I think I got it, the COS part cancel out leaving just the 4pi/5 parts.

My end result is then:

[(4pi/5)^3 / 3] + [(4pi/5)^3 / 3]

I am trying to simplify this and have some trouble. I turned it into:

2 * [(4pi/5^3) * 3]

Can it be simplified further?
• Oct 3rd 2010, 12:16 PM
skeeter
Quote:

Originally Posted by solidstatemath
I'm having trouble simplifying this.

I got:

[(4pi/5)^3 / 3] - [COSpi4/5] - [(-4pi/5)^3 / 3] - [-COS(-4pi/5)]

I think the COS term will cancel out and then we get 2[(4pi/5)^3 / 3] as the answer.

Things I am not sure about: the signs. I'm not sure about:

- [-COS(-4pi/5)] *** does this become positive? What about the -4pi/5?

cosine is an even function ... $\displaystyle \cos(-x) = \cos(x)$
• Oct 3rd 2010, 12:36 PM
solidstatemath
Skipping the details here, the format above would then be the first term with pi - cosine term + second pi term + second cosine term.

The is the most I can simplify it: 2 * [(4pi/5^3) * 3]

How does this look? Basically the cosine terms cancel out and leaves just 2 times the pi terms.