# hw4 - Z ∞ dx x p 4.5 Determine whether the improper...

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 4. Due February 5. 4.1. Evaluate Z 1 0 xdx 2 - x 4 4.2. Evaluate Z y 3 + 1 y 3 - y 2 dy 4.3. Determine whether the following improper integrals converge or diverge. Evaluate the integral if it converges. (i) Z 2 dx x 2 - 1 (ii) Z 0 cos2 xdx (iii) Z 1 arctan x x 2 dx 4.4. (i) Investigate the convergence of the integral Z 1 0 dx x p for diﬀerent values of p > 0. (ii) Use (i) and properties of Z 1 dx x p to determine convergence of
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Unformatted text preview: Z ∞ dx x p 4.5. Determine whether the improper integral Z ∞ 1 sin 2 3 x 3 √ x 4 + 1 dx converges or diverges. Do not evaluate the integral if it converges. 4.6. Use the identity Z ∞-∞ e-x 2 dx = √ π to evaluate Γ(1 / 2) and Γ(5 / 2). For relevant deﬁnitions see Lecture 3 of the Course Notes. 1...
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