salmanhiro

UTS 2 Matematika IIA ITB 2017 (Bagian A nomor 5)

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\begin{align*}\int_{0}^{2}\int_{0}^{y}(xy+y^2)\,dx\,dy&=\int_{0}^{2}\left[\frac{y}{2}x^2+y^2x\right]_{0}^{y}\,dy\\&=\int_{0}^{2}\left(\frac{y^3}{2}+y^3\right)\,dy\\&=\int_{0}^{2}\frac{3}{2}y^3\,dy\\&=\left[\frac{3}{8}y^4\right]_{0}^{2}\\&=\boxed{6}.\end{align*}

 

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