Question

Integrate 1/sqrt(3-x) from 2 to 3

Answer 1

\[\int\limits_{2}^{3}\frac{1}{\sqrt{3-x}} dx\]

Answer 2

let u=3-x
=>
du=-1 dx

Answer 3

so if du=-1 dx
then
-du=1 dx

Answer 4

\[\int\limits_{3-2}^{3-3}\frac{-du}{\sqrt{u}}\]

Answer 5

\[-\int\limits_{1}^{0}u^\frac{-1}{2} du=-2u^\frac{1}{2}|_1^0=-2(0^\frac{1}{2}-1^\frac{1}{2})=-2(-1)=2\]