- #1
eclayj
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Homework Statement
Calculate the following integral exactly (no approximations) by the method of integration by parts:
∫0t SinIntegral[x] dx
Homework Equations
the following hints are given:
D[SinIntegral[x], x] = Sinc[x]; and
SinIntegral[0] = 0
The Attempt at a Solution
The integration by parts forrmula is ∫abu[x]v'[x]dx = u[x]v[x]|ab-∫abv[x]u'[x]dx.
The problem I have is that whether I let u[x]=1 and v'[x]= SinIntegral[x], or u[x]=SinIntegral[x] and v'[x]= 1, either way the integral on the right is more complex than what I started with (either ∫0txSinc[x]; or ∫0tSinIntegral[x].
Any help is appreciated. I hope all the programming tags work here, otherwise this will look like a mess. It may still look like a mess
So it seems to me that, although the question requires the differentiation by parts method, such method does not work because it you get more complicated integrals