Question

Determine integral dupla

Answer 1

Resolva por partes, primeiro o x depois o y:

Answer 2

C.

Explicação passo a passo:

$\displaystyle\int_0^{2} \int_1^4 xy^2 \; dx dy=\displaystyle\int_0^{2} \Bigg[\dfrac{x^2}{2} y^2\Big|_1^4\Bigg]dy=\displaystyle\int_0^{2} \Bigg[\dfrac{4^2}{2} y^2-\dfrac{1^2}{2} y^2\Bigg]dy=\\\\\\=\displaystyle\int_0^{2} \dfrac{15}{2} y^2\;dy=\dfrac{15}{2}\displaystyle\int_0^{2} y^2\;dy=\dfrac{15}{2} \bigg(\frac{y^3}{3}\Big|_0^2 \bigg)=\dfrac{15}{2} \bigg(\frac{2^3}{3}-\dfrac{0^3}{3} \bigg)=\dfrac{15}{2} \cdot\dfrac{8}{3} =\\\\\\=\dfrac{120}{6}=20$