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AP Calculus BC/Unit 8: Applications of Integration
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Improper Integral Convergence With a Parameter

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For which values of pp does the improper integral ∫0∞xp1+x2 dx\displaystyle\int_0^{\infty} \frac{x^p}{1+x^2} \, dx converge?

A

−1<p<1\displaystyle -1 < p < 1

B

p>0\displaystyle p > 0

C

p>−1\displaystyle p > -1

D

p<1\displaystyle p < 1

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