integal of (cosx-sinx)/sqrt(cox+sinx)?

Question

How should I go about this?

Answer 1

Let u = cosx + sinx

du =( -sinx + cosx)dx

Therefore, the above integral can be written as

integral (1/sqrt(u)) du

This is equal to 2* sqrt(u) + c, but u = cosx + sinx

Therefore, the answer is 2*sqrt(cosx + sinx) + c

Answer 2

First note that this is 2 separate integrals; one with cosx in the numerator and the other with -sinx in the numerator.

This is a huge simplification. Use a substitution method as suggested above and you will get the correct answer, which has not been given yet..........

Answer 3

let sinx+cos x=t
differentiate,
hence, (cosx- sin x)dx= dt
substitute in ques.
hence ques becomes integral of dt/ sq root t
therefore answer is 2 times sq root t+ C
ie, 2 times sq root (sin x +cos x) +C

Answer 4

put cosx+sinx=t
(cosx-sinx)dx=dt
integral dt/(t)^1/2
=2(t)^1/2+C
=2(cosx+sinx)^1/2+C

Answer 5

The same way porcupines copulate.........Very carefully.

Prune has the right of it.


Doug