Tough Integral

Integrate [(c+x)/(c-x)]^.5 from -c to c

Question

Tough Integral

Integrate [(c+x)/(c-x)]^.5 from -c to c

anonymous · Answer

$$\int\limits_{-c}^{c}\sqrt{\frac{ c+x }{c-x }}dx$$

anonymous · Answer

$$\int\limits_{-c}^{c} \sqrt{(\frac{c+x}{c-x})}dx$$
try
$$x=c \times \cos(2t)$$$$dx=-2csin(2t)dt$$

anonymous · Answer

I will Thanks

anonymous · Answer

So it's been a really long time since I've done substitution. How do I change the constants of integration?

anonymous · Answer

What do you mean?This a definite integral so you wouldn't have any constant of integration

anonymous · Answer

Sorry I mean the interval$$\int\limits_{-c}^{c} \rightarrow \int\limits_{?}^{?}$$

michele_laino · Answer

Please try this substitution:
$$\frac{{c + x}}{{c - x}} = {t^2}$$
where t is the new variable of integration

anonymous · Answer

sorry, to change the limits put
$$x=c$$ and $$x=-c$$ find the value in terms of t for the corresponding limit

anonymous · Answer

what would dt be?

anonymous · Answer

This is for a fracture mechanics question. My professor said he substituted b=x/c and db=dx/c and it worked out great but I cant seem to get this