Alguem pode ajudar na solução das integrais

postei la no meu as resposta

Para solucionarmos a integral dada, realizaremos os cálculos abaixo:

\(\begin{array}{l} f(x,y) = ysenx\\ \\ \int_{}^{} {\int_{}^{} {f(x,y)} = \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } } \\ \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } = \int_0^{\pi /2} {\left( {\frac{{{y^2}}}{2}\sin x} \right)_0^1} \\ \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } = \int_0^{\pi /2} {\left( {\frac{1}{2}\sin x} \right)} \\ \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } = \frac{1}{2}\left( {\cos x} \right)_0^{\pi /2}\\ \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } = \frac{1}{2}\cos \pi /2\\ \int_0^{\pi /2} {\int_0^1 {\left( {ysenx} \right)dydx} } = \frac{1}{2} \end{array}\)