Question

求解变限积分公式

如果所示，积分的上下限均为变量，y也是变量求，y与t的函数关系

Answer 1

∫<t, t+y>e^(at)dt = (1/a)[e^(at)]<t, t+y> = (1/a){e^[a(t+y)] - e^(at)}
= (1/a)e^(at)[e^(ay)-1] = v, 得 e^(at)[e^(ay)-1] = av，
y = (1/a)ln[1+ave^(-at)]

Answer 2

V=(1/a)e^at=(1/a)(e^a(t+y)－e^at)
=(e^at)/a(e^ay－1)
即e^ay－1=aVe^(－at)