Thread: 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



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

second one



let

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

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.

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?