Scary integrals with multiple solving techniques

[bdou]

1. i have three different integrals that i need help solving to finish my calc 2 extra credit:
1. [tex]\intx\sqrt{4-x}[\tex]
-solve using trig substitution
-solve using substitution

2. lim x[tex]\rightarrow\infty[\tex] [txt]xe^-x^2[\txt]
-solve (using L'Hopital's??)


3. [tex]\int\frac{x}{1+e^{2x}}[tex]

Homework Equations

The Attempt at a Solution

1. for the first i have no clue how to change it to trig, however i started the second part by using u=4-x to begin?

2. I'm unsure as how to use L'Hopital's, i was absent that day in class and could use a general overview as well

3. i don't know how to start-i have a feeling i have to change it into one of the integral forms in the back of my calc book-however it doesn't fit any of the formulas

 

[rocomath]

your latex is messed up ... it should be [/tex]

and you should show work b4 receiving help. please read your book.

 

[Gib Z]

Welcome to Physics Forums bdou! You will find there are many people on the forums only too willing to help, but that is all we do. We do not do your homework for you. So please show us some working next time.

It seems for these questions you have exactly no clue at all, so some hints may help you show us some working.

For the first one: Post 3 has one method, the trig one is to use The trig Pythagorean identities. Notice 4 is a perfect square. What trig function can we let x be so the square root becomes eliminated?

For the second one, L'hopitals rule basically states that if the function in the limit is in an indeterminate form: $$\frac{0}{0}, \frac{ \pm \infty}{\pm \infty}$$, then $$\lim_{x\to a} \frac{ f(x)}{g(x)} = \lim_{x\to a} \frac{ f'(x)}{g'(x)}$$. For the limit you have, it happens to be infinity on infinity case. Of course you don't actually need the rule here, notice the rates of growth of these functions.

For the third one, try integration by parts.