Definite Integration Question - None

Question

Evaluate $\int_{2}^{3} \frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}} dx$

Accepted Answer

$I = \int_{2}^{3} \frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}} dx$
$I = \int_{2}^{3} \frac{\sqrt{3+2-x}}{\sqrt{5-(3+2-x)}+\sqrt{3+2-x}} dx$
$I = \int_{2}^{3} \frac{\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}} dx$
$2I = \int_{2}^{3} \left( \frac{\sqrt{5-x}+\sqrt{x}}{\sqrt{x}+\sqrt{5-x}} \right) dx \Rightarrow 2I = \int_{2}^{3} dx$
$2I = (x)_{2}^{3} \Rightarrow 2I = 1$
$I = \frac{1}{2}$

Question:

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