Help with Integral Problems

I have three in particular, two of which I can't seem to get anywhere and another which I think I may have domain issues.

-Just for reference, I can only solve these using u-substitution or through anti-derivatives that we've memorized. (i.e. sinx'=cosx, x^n'=n-1x^n-1, etc.)

1.)

I've tried u-substitution for this one but when finding du/dx nothing seems to replace every t variable to simplify into something that's easy to integrate. I've tried rewriting but rewriting it makes it even more complicated. (I've tried rewriting tan(t) into sin(t)/cos(t), I've tried to split up the problem, but no avail, nothing seems to work) A few tips on how to start would greatly help!!

2.)

On this one, I've tried u-substitution with the denominator & numerator portion of the function:

u=1+e^2x

du/dx=e^2x * 2

1/2du=e^2x dx

or

u=e^x

du=e^x dx

Neither one replaces every x variable in the original function so I'm stuck there.

3.)

This last one I was able to integrate but once I start evaluating for the x intervals it asks for I get a domain issue. After integrating and using u-substitution I get

F(x) = 1/2 ln (x^2 - 4) from x-values 10 and 1.

When plugging in 10 I get a positive value which is solvable; however, when plugging in 1 I get a negative value which isn't defined at ln(x).

Nevermind, solved this one (Happy)

-All the help and assistance will be greatly appreciated!!!

Re: Help with Integral Problems

Re: Help with Integral Problems

The first one cannot be solved in terms of the standard functions. The third one is undefined.

Re: Help with Integral Problems

Quote:

Originally Posted by

**princeps** The first one cannot be solved in terms of the standard functions. The third one is undefined.

Thank you, I kinda of find it odd that our would teacher would assign that problem considering we haven't covered the material necessary to solve it, but then again, we had a similar issue with a different problem that could not be solved with standard functions, and she let us omit it :). I'll just bring it to her attention tomorrow in class.

Re: Help with Integral Problems

Quote:

Originally Posted by

**dagbayani481** I have three in particular, two of which I can't seem to get anywhere and another which I think I may have domain issues.

-Just for reference, I can only solve these using u-substitution or through anti-derivatives that we've memorized. (i.e. sinx'=cosx, x^n'=n-1x^n-1, etc.)

1.)

I've tried u-substitution for this one but when finding du/dx nothing seems to replace every t variable to simplify into something that's easy to integrate. I've tried rewriting but rewriting it makes it even more complicated. (I've tried rewriting tan(t) into sin(t)/cos(t), I've tried to split up the problem, but no avail, nothing seems to work) A few tips on how to start would greatly help!!

The integrand is an odd function, and you are integrating over a symmetric interval. Can you infer anything from that?