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# AP Calculus BC: p-int practice worksheet

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### AP Calculus BC: p-int practice worksheet

1. 1. p-Integrals In Practice4 Confirm Theorem 3.1 Analytically (use anti-derivatives): 1 Show ⌠ dx 14.1  x= 1=2 ⌡ 1- 0 2 1 Show ⌠ dx 1 34.2 = = 3 1 2 ⌡ x 1-3 0 a:pintprac.doc 1
2. 2. p-Integrals In Practice5 Confirm Theorem 3.3 Analytically (use anti-derivatives): ∞ Show ⌠ 2 = dx 15.1 =1 ⌡ x 2-1 1 ∞ Show ⌠ 3 = dx 1 15.2 = ⌡ x 3-1 2 1 a:pintprac.doc 2
3. 3. p-Integrals In Practice6 Confirm Corollary 3.2 Numerically (use convergence/divergence tables): 1 Show ⌠ dx6.1 Diverges. ⌡ x2 0 1 Show ⌠ 3 Diverges. dx6.2 ⌡x 0 a:pintprac.doc 3
4. 4. p-Integrals In Practice7 Confirm Corollary 3.2 Numerically (use convergence/divergence tables): ∞ Show ⌠ dx7.1  Diverges. ⌡ x 1 ∞ Show ⌠ dx7.2 Diverges. 3 ⌡ x 1 a:pintprac.doc 4
5. 5. p-Integrals In Practice8 For each of the following p-Integrals, apply the appropriate Theorem or Corollary to demonstrate convergence or divergence. Using a method of your choice (analytical or numerical) confirm your results. 18.1 ⌠ dx 3 ⌡ x2 0 ∞8.2 ⌠ dx 3 ⌡ x2 1 1 ⌠ dx8.3  x3 ⌡ 0 ∞ ⌠ dx8.4  x3 ⌡ 1 a:pintprac.doc 5