Respuesta :

The average value is given by

[tex]\displaystyle\frac1{10-4}\int_4^{10}\cos^{13}5t\sin5t\,\mathrm dt[/tex]

Setting [tex]y=\cos5t[/tex], you get [tex]\mathrm dy=-5\sin5t\,\mathrm dt[/tex], and the integral becomes

[tex]\displaystyle-\frac1{30}\int_{\cos20}^{\cos50}y^{13}\,\mathrm dy[/tex]
[tex]=-\dfrac1{30}\dfrac{y^{14}}{14}\bigg|_{y=\cos20}^{y=\cos50}[/tex]
[tex]=-\dfrac{\cos^{14}50-\cos^{14}20}{420}\approx-0.00145[/tex]
ACCESS MORE
EDU ACCESS
Universidad de Mexico