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### definite integral and indefinite integral different (~Gaussian)

Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated.

Here comes the important and irritating part: $f4 = f2(a=3,N=0.7); f4$ (e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2 $Z = integral(f4,y,-100,100); Z.n(digits=5)$ 9.7000 $F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)$ -1.1562e-14

I guess it is not important, but the part mentioned above is prepared with $f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$ e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N) $f2 = f1y^2; f2$ (e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))y^2

### definite integral and indefinite integral different (~Gaussian)

Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated.

Here comes the important and irritating part: part:

$f4 = f2(a=3,N=0.7); f4$ (e^(-0.714285714285714f4(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2 3)^2))*y^2Z = integral(f4,y,-100,100); Z.n(digits=5)$9.7000 Z.n(digits=5)$

$9.7000$

$F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)$ -1.1562e-14

H.n(digits=5)-1.1562e-14$I guess it is not important, but the part mentioned above is prepared with$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N)$f2 = f1y^2; f2$(e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))y^2 ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated. Here comes the important and irritating part:$f4 = f2(a=3,N=0.7); f4(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + + 3)^2))*y^2Z = integral(f4,y,-100,100); Z.n(digits=5)9.7000F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)-1.1562e-14$I guess it is not important, but the part mentioned above is prepared with$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N)$f2 = f1y^2; f2$(e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))y^2 ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated. Here comes the important and irritating part:$f4 = f2(a=3,N=0.7); f4(e^(-0.714285714285714(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2$3)^2))*y^2$Z = integral(f4,y,-100,100); Z.n(digits=5)9.7000$9.7000$F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)-1.1562e-14$-1.1562e-14 I guess it is not important, clear even so, but here is the part before what is mentioned above is prepared with above:$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$f1$

e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N) y)^2/N)

$f2 = f1y^2; f2$ f1*y^2; f2$(e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))y^2 (a + y)^2/N))*y^2 ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated. Here comes the important and irritating part:$f4 = f2(a=3,N=0.7); f4$(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2$Z = integral(f4,y,-100,100); Z.n(digits=5)$9.7000$F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)$-1.1562e-14-2.4622e-2917 I guess it is clear even so, but here is the part before what is mentioned above:$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N)$f2 = f1*y^2; f2$(e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))*y^2$f4 = f2(a=3,N=0.7); f4$(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2 ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated. Here comes the important and irritating part:$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1f2 = f1*y^2; f2f4 = f2(a=3,N=0.7); f4$(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2$Z = integral(f4,y,-100,100); Z.n(digits=5)$9.7000$F = integrate(f4,y); H = F(y=10) - F(y=-10); H.n(digits=5)$-2.4622e-2917 As you see, I guess get right results when using the definite integral, while calculation the indefinite integral and manually evaluating it is clear even so, but here is the part before what is mentioned above:$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N)$f2 = f1*y^2; f2$(e^(-1/2(a - y)^2/N) + e^(-1/2(a + y)^2/N))*y^2$f4 = f2(a=3,N=0.7); f4$(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2 gains wrong results. By the way, when integrating from -inf to inf, I should get N+a^2. Is there any way to see this? ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated.$f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1f2 = f1*y^2; f2f4 = f2(a=3,N=0.7); f4$(e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2$Z = integral(f4,y,-100,100); Z.n(digits=5)$9.7000$F = integrate(f4,y); H = F(y=10) F(y=100) - F(y=-10); F(y=-100); H.n(digits=5)$-2.4622e-2917 As you see, I get right results when using the definite integral, while calculation the indefinite integral and manually evaluating it gains wrong results. By the way, when integrating from -inf to inf, I should get N+a^2. Is there any way to see this? ### definite integral and indefinite integral different (~Gaussian) Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated.$f1

 f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1$   $f2 f1

 f2 = f1*y^2; f2f4 f2 f4 = f2(a=3,N=0.7); f4$f4 (e^(-0.714285714285714(y - 3)^2) + e^(-0.714285714285714(y + 3)^2))*y^2$Z Z = integral(f4,y,-100,100); Z.n(digits=5)$Z.n(digits=5) 9.7000$F F = integrate(f4,y); H = F(y=100) - F(y=-100); H.n(digits=5)\$ H.n(digits=5)



-2.4622e-2917



As you see, I get right results when using the definite integral, while calculation the indefinite integral and manually evaluating it gains wrong results.

By the way, when integrating from -inf to inf, I should get N+a^2. Is there any way to see this?

 9 No.9 Revision calc314 4101 ●20 ●47 ●109

### definite integral and indefinite integral different (~Gaussian)

Hello, I get strange behaviour on the following function. It persists when changing constants, but is not present for very simple functions, so any hint for a limit would be appreciated.

 f1 = exp(-1/2(y-a)^2/N)+exp(-1/2(y+a)^2/N); f1exp(-1/2*(y-a)^2/N)+exp(-1/2*(y+a)^2/N); f1
f2 = f1*y^2; f2f2
f4 = f2(a=3,N=0.7); f4  (e^(-0.714285714285714(y f4
>(e^(-0.714285714285714*(y - 3)^2) + e^(-0.714285714285714(y e^(-0.714285714285714*(y + 3)^2))*y^23)^2))*y^2
Z = integral(f4,y,-100,100); Z.n(digits=5)Z.n(digits=5)
>9.7000
9.7000  F = integrate(f4,y); H = F(y=100) - F(y=-100); H.n(digits=5) H.n(digits=5)
>-2.4622e-2917
 -2.4622e-2917 

As you see, I get right results when using the definite integral, while calculation the indefinite integral and manually evaluating it gains wrong results.

By the way, when integrating from -inf to inf, I should get N+a^2. N+a^2. Is there any way to see this?