definite integration(2)
2011-03-10 1:33 am
It is given that f(x) is a periodic continuous function with period T. Let a and b be real numbers where a<b, k is a positive integer. Prove that ∫(e^x)f(x) dx [upper limit is b+kT, lower limit is a+kT]= (e^kT)∫(e^x)f(x) dx [upper limit is b, lower limit is a]
回答 (2)
2011-03-10 2:24 am
✔ 最佳答案
Solution:Let u = x - kT.
du = dx , x = a + kT, u = a ; x = b + kT, u = b
∫(e^x)f(x) dx [a + kT, b + kT]
= ∫e^(u + kT) f(u + kT) du [a , b]
= e^(kT) ∫e^u f(u) du [a , b]
= e^(kT) ∫e^x f(x) dx [a , b]
2011-03-10 1:35 am
收錄日期: 2021-04-16 12:22:48
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