integral de pi a 5pi de x^2sin(x)

Solución

\int_{π}^{5 π} x^{2} sin (x) d x

24 π^{2}

Decimal

236.87050 \dots

Pasos de solución

\int_{π}^{5 π} x^{2} sin (x) d x

Aplicar integración por partes

= [- x^{2} cos (x) - \int - 2 x cos (x) d x]_{π}^{5 π}

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= [- x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))]_{π}^{5 π}

Simplificar

= [- x^{2} cos (x) + 2 (x sin (x) + cos (x))]_{π}^{5 π}

Calcular los limites:

24 π^{2}

= 24 π^{2}