Evalúe la integral doble iterada

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Hola alfonso!

$$\begin{align}&\int_1^4 \Bigg[ \int_{y^2}^y \sqrt{\frac y x}\ dx \Bigg]dy=\\&\\&\int_1^4 \Bigg [ \sqrt y \int_{y^2}^y\ x^{-\frac 1 2}\ dx \Bigg]dy=\\&\\&\int_1^4 \sqrt y\ \Bigg [2x^\frac 1 2 \Bigg]_{y^2}^y dy=\\&\\&2 \int_1^4 \sqrt y \Bigg[y^\frac 1 2-y\Bigg] dy=\\&\\&2\int_1^4 \Big(y-y^\frac 3 2 \Big) dy=\\&\\&2\Bigg[ \frac{y^2} 2- \frac 2 5y^\frac 5 2 \Bigg]_1^4=\\&\\&2\Bigg[8-\frac 2 5•32- \Big( \frac 1 2 - \frac 2 5\Big) \Bigg]=- \frac {49} 5\end{align}$$

Saludos

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