Math& 152 Spring 2023 "Techniques of Integration" Challenge Set INSTRUCTIONS: Please do your work on a separate sheet or sheets of paper. To receive full credit, a problem must be solved correctly and completely, with all relevant work shown; solutions should be clear, concise, and thorough. Use complete sentences as appropriate. Sloppy or incomplete work will not receive full credit, even if the solution is correct. You are strongly encouraged to make use of rough drafts before writing up your nal submission. Your answer to each question should include the following: o A statement of which strategy or strategies you are using (i.e. which "type" of problem this is) o A clear indication of any steps you took to modify the integrand (including any sub- stitutions) o A clear indication of how you are applying any substitutions Evaluate the following indenite and denite integrals: 1. f 33"; sin(2:c}dz: 2fmd" IH+2+31+4 3 l z(+1}2(x2+1}d33 4 z 4. f1 'jdx TI' . 5. In sm2 3 cos4 2: d2? It may be helpful to recall that sin23: 2 {1 cos 23:} and/or that cosQa: = % (1 + cos 2:33) Math& 152 "Techniques of Integration" Challenge Set [END OF SET]