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10. Using the indicated techniques to evaluate the following integrals. Show work detail to support your solutions. Solving using other methods or with no detail
10. Using the indicated techniques to evaluate the following integrals. Show work detail to support your solutions. Solving using other methods or with no detail is not acceptable. (a) Ii v9x2+4 (Trigonometric substitution) 2 (b) Jxzdx (Trigonometric substitution) l6 x J (c) I x2 In xdx (Integration by Parts) 11. Complete the square in the denominator, make appropriate substitution, and integrate the integral [x .7: + x+ 5 12. Find the partial fraction decomposition for the rational function and (u - 2)(u + 3) then evaluate the integral [+19% (u 2)(u + 3) 13. State whether the sequence converges or diverges. If it converges, nd its limit. 2 2 {mmzmm} n 14. Using the Integral Test to test the following series for convergence. Solving using other methods or with no detail is not acceptable. \" 1 \"=3 n(ln rt)2 15. Determine whether the following series converge or diverge. Indicate the test you use. (b) E "in" +2M2 2 16. Determine whether the series i [[1] [ %] ] converges or diverges. If it \"=0 converges, nd its sum. 1?. Determine whether the series 2( "=U\\/:1+3 absolutely, or diverges and give reasons for your conclusions. converges conditionally, or converges I! x 18. Find the interval of convergence for the power series 2 1 2 \"-0 n + cit-1 I 19. Use substitution method and a known power series to nd power series for Please express your answer in one sigma notation
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