Question

这个积分怎么解 谢谢

Answer 1

∫(0->π/2)sinadsina
=∫(0->π/2)1/2*2sinadsina
=∫(0->π/2)1/2d(sina)^2
=(sina)^2 /2 |(0->π/2)
=1/2

∫(0->1)r^3e^-r^2 dr
=∫(0->1)r^2e^-r^2*rdr
=-1/2∫(0->1)r^2e^-r^2*d(-r^2)
=-1/2∫(0->1)r^2de^-r^2)
=-1/2*r^2e^-r^2+1/2∫e^-r^2dr^2
=-1/2*r^2e^-r^2-1/2∫e^-r^2d-r^2
=-1/2*r^2e^-r^2-1/2e^-r^2
=-e^-r^2 / 2 *(r^2+1) |(0->1)
=-(e^-1 /2 *2 - e^-0 /2 * 1)
=-(1/e -1)
=1-1/e

两式相乘？
相乘就是
1/2*(1-1/e)
=1/2-1/(2e)