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Question: Why doesn't Maple evaluate the integral of this sum as a sum of integrals?

Question:Why doesn't Maple evaluate the integral of this sum as a sum of integrals?

Angelo Melino 45 Maple 2019
integration
February 06 2020
1

I'm using MAPLE 2019 and I'm sometimes surprised by its behaviour.  For example, I appear to have an example where it evaluates the integral of each of two terms but not their sum...  What's going on?  Please see the attached.

restart

g0 := exp(r*cos(theta))/Pi

exp(r*cos(theta))/Pi

 (1)

G0 := `assuming`([int(g0, theta = 0 .. Pi)], [r > 0])

BesselI(0, r)

 (2)

g1 := exp(r*cos(theta))*cos(theta)/Pi

exp(r*cos(theta))*cos(theta)/Pi

 (3)

G1 := `assuming`([int(g1, theta = 0 .. Pi)], [r > 0])

BesselI(1, r)

 (4)

g := g0+g1

exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi

 (5)

G := `assuming`([int(g, theta = 0 .. Pi)], [r > 0])

int(exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi, theta = 0 .. Pi)

 (6)

``


 

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