# Trig substition confusion

1. Oct 27, 2006

### sapiental

Hi

If I have the indefinite integral x(sqrt(4-x^2))dx

must I replace x with 2sint and then dx = 2cosdt

or can I just do regular substitution with u = 4-x^2 since xdx occurs in the integral already.

when I solve it this way I get -1/3(4-x^2)^3/2 + C

it just seems alot more work to do it the trigonometric substitituon way.

Any help is much appreciated. Thanks!!

2. Oct 27, 2006

you have to use the substitution $$x = 2\sin \theta$$.

Thus $$dx = 2\cos \theta d\theta$$.

At the end you have to solve for $$\theta$$ to convert the integral back in terms of x. you know that $$\sin \theta = \frac{x}{2}$$, so use a right triangle to express this relationship.

Last edited: Oct 27, 2006
3. Oct 27, 2006

### sapiental

hey,

are you positive? My professor Just emailed me saying that the substitution u = 4-x^2 is acceptable.

Did you miss my x infront of the sqrt(4-x^2)dx ?

Really confused now..

4. Oct 27, 2006

### arildno

There is nothing wrong with your own substitution.
You might check, though, that the two substitutions yield the same answer.