Calculate The Following Integral

Hello! The problem is:

Calculate The Following Integral:

(e^x + e^-x) from ln2 to ln3.

I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right? Or maybe I'm starting horrible hence why I can't solve it.

Thanks in advance for any help! I've been stuck only on this one problem for hours!

re: Calculate The Following Integral

Quote:

Originally Posted by

**antz215** Hello! The problem is:

Calculate The Following Integral:

(e^x + e^-x) from ln2 to ln3.

I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right?

You can always find help here.

Know that $\displaystyle e^{\ln(3)}=3~\&~e^{-\ln(3)}=\frac{1}{3}~.$

re: Calculate The Following Integral

Quote:

Originally Posted by

**antz215** Hello! The problem is:

Calculate The Following Integral:

(e^x + e^-x) from ln2 to ln3.

I'm pretty sure the next step is to change it to (e^x - e^-x) as those are the anti-derivatives right? Or maybe I'm starting horrible hence why I can't solve it.

Thanks in advance for any help! I've been stuck only on this one problem for hours!

It's easy to check isn't it: the derivative of $\displaystyle e^x- e^{-x}$ is $\displaystyle e^x-(-1)e^{-1}= e^x+ e^{-x}$ so yes, **an** anti-derivative of $\displaystyle e^x+ e^{-x}$ is $\displaystyle e^x- e^{-x}$.

Fundamental theorem of Calculus: if F(x) is an anti-derivative of f(x) then $\displaystyle \int_a^b f(x)dx= F(b)- F(a)$.

re: Calculate The Following Integral

From both helps I am getting:

e^x + e^-x dx

(e^x - e^-x)

(e^ln3 - e^-ln3) - (e^ln2 - e^-ln2)

3 - 1/3 - 2 + 1/2

= 7/6

I think that is correct? Thanks for your guys' help!

Re: Calculate The Following Integral

Yes, that is correct. Congratulations!