Calculus II·Convergence of Improper Integrals
Improper Integral Convergence by p-Test
Given the improper integral ∫_a^∞ c/x^p dx, decide whether it converges and, if so, compute its value. Convergence is determined by the p-test: the integral converges iff p > 1.
✓ All 6 test cases pass.
Inputs
Test cases
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| # | Inputs | Expected | Got | Status |
|---|---|---|---|---|
| 1 | {"c":1,"p":2,"a":1} | 1 | 1 | ✓ |
| 2 | {"c":1,"p":3,"a":1} | 0.5 | 0.5 | ✓ |
| 3 | {"c":2,"p":2,"a":1} | 2 | 2 | ✓ |
| 4 | {"c":1,"p":2,"a":2} | 0.5 | 0.5 | ✓ |
| 5 | {"c":1,"p":1,"a":1} | diverges (p ≤ 1) | diverges (p ≤ 1) | ✓ |
| 6 | {"c":1,"p":0.5,"a":1} | diverges (p ≤ 1) | diverges (p ≤ 1) | ✓ |
Source: Pattern: p-integral test. Reproduces the standard Cal II result, e.g. Stewart 'Calculus' 8e §7.8.
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