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A definite integral across a pole is answered with a finite value: 1/x^2 over [-1, 1] is -2 #1508
Description
integral(1/x^2, x, -1, 1) simplifies to -2. The integrand is positive, and the integral diverges to +oo.
The antiderivative -1/x is evaluated at the two bounds, and the pole between them is never seen. BreakpointIntegration splits the range at the jumps of floor, ceil and piecewise, but not at a point where the integrand is undefined.
| integral | master | value |
|---|---|---|
1/x^2 over [-1, 1] |
-2 |
+oo |
tan(x) over [0, 3] |
-ln(cos(3)) |
none: a pole at pi/2 |
1/(x - 2) over [0, 3] |
-ln(-2) |
none: a pole at 2 |
1/x over [-1, 1] |
-ln(-1) |
none: -oo and +oo on either side of 0 |
Activity
A definite integral is taken piece by piece across its antiderivative…