1. ## Integrtion

Integrate √(5+4x-x^2)

I dont even know where to begin. Any ideas?

2. $\displaystyle \int \sqrt{5+4x-x^2}dx = \int \sqrt{9-(x-2)^2}dx$

Now use u and trignometric substitution

3. Originally Posted by andrewho93
Integrate √(5+4x-x^2)

I dont even know where to begin. Any ideas?
When you see something with $x^2$ as the largest power or in any case where you may complete the square e.g $x^4+2x^2+3=(x^2+1)^2+2$. Then you want use a trig substitution. A trig substition involves a squared term and a constant. This is useful when the whole term is bracketed by a power which makes the normal integration complex.

$\int \sqrt{5+4x-x^2} = \int \sqrt{9-(x-2)^2}$
let $x-2=\frac{sinx}{3}$