Question

计算函数y=2xe-x在[0,2]上的平均值

Answer 1

y平均=[∫2xe^(-x)dx]/(2-0)

=∫xe^(-x)dx

=-∫xde^(-x)

=[-xe^(-x)]+∫e^(-x)dx

=[-xe^(-x)]-∫e^(-x)d(-x)

=[-xe^(-x)]-[e^(-x)]

=-2e^(-2)-[e^(-2)-1]

=-3e^(-2)+1