{"id":159,"date":"2026-01-12T15:56:09","date_gmt":"2026-01-12T15:56:09","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=159"},"modified":"2026-01-12T15:56:09","modified_gmt":"2026-01-12T15:56:09","slug":"physical-applications-of-integration-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/physical-applications-of-integration-get-stronger-answer-key\/","title":{"raw":"Physical Applications of Integration: Get Stronger Answer Key","rendered":"Physical Applications of Integration: Get Stronger Answer Key"},"content":{"raw":"

Physical Applications<\/h2>\r\n
    \r\n \t
  1. [latex]150[\/latex] ft-lb<\/li>\r\n \t
  2. [latex]200\\text{J}[\/latex]<\/li>\r\n \t
  3. [latex]1[\/latex] J<\/li>\r\n \t
  4. [latex]\\frac{39}{2}[\/latex]<\/li>\r\n \t
  5. [latex]\\text{ln}(243)[\/latex]<\/li>\r\n \t
  6. [latex]\\frac{332\\pi }{15}[\/latex]<\/li>\r\n \t
  7. [latex]100\\pi [\/latex]<\/li>\r\n \t
  8. [latex]20\\pi \\sqrt{15}[\/latex]<\/li>\r\n \t
  9. [latex]6[\/latex] J<\/li>\r\n \t
  10. [latex]5[\/latex] cm<\/li>\r\n \t
  11. [latex]36[\/latex] J<\/li>\r\n \t
  12. [latex]18,750[\/latex] ft-lb<\/li>\r\n \t
  13. [latex]\\frac{32}{3}\u00d7{10}^{9}\\text{ft-lb}[\/latex]<\/li>\r\n \t
  14. [latex]8.65\u00d7{10}^{5}\\text{J}[\/latex]<\/li>\r\n \t
  15. \r\n
      \r\n \t
    1. [latex]3,000,000[\/latex] lb,<\/li>\r\n \t
    2. [latex]749,000[\/latex] lb<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    3. [latex]23.25\\pi [\/latex] million ft-lb<\/li>\r\n \t
    4. [latex]\\frac{A\\rho {H}^{2}}{2}[\/latex]<\/li>\r\n \t
    5. Answers may vary<\/li>\r\n<\/ol>\r\n

      Moments and Centers of Mass<\/h2>\r\n
        \r\n \t
      1. [latex]\\frac{5}{4}[\/latex]<\/li>\r\n \t
      2. [latex](\\frac{2}{3},\\frac{2}{3})[\/latex]<\/li>\r\n \t
      3. [latex](\\frac{7}{4},\\frac{3}{2})[\/latex]<\/li>\r\n \t
      4. [latex]\\frac{3L}{4}[\/latex]<\/li>\r\n \t
      5. [latex]\\frac{\\pi }{2}[\/latex]<\/li>\r\n \t
      6. [latex]\\frac{{e}^{2}+1}{{e}^{2}-1}[\/latex]<\/li>\r\n \t
      7. [latex]\\frac{{\\pi }^{2}-4}{\\pi }[\/latex]<\/li>\r\n \t
      8. [latex]\\frac{1}{4}(1+{e}^{2})[\/latex]<\/li>\r\n \t
      9. [latex](\\frac{a}{3},\\frac{b}{3})[\/latex]<\/li>\r\n \t
      10. [latex](0,\\frac{\\pi }{8})[\/latex]<\/li>\r\n \t
      11. [latex](0,3)[\/latex]<\/li>\r\n \t
      12. [latex](0,\\frac{4}{\\pi })[\/latex]<\/li>\r\n \t
      13. [latex](\\frac{5}{8},\\frac{1}{3})[\/latex]<\/li>\r\n \t
      14. [latex]\\frac{m\\pi }{3}[\/latex]<\/li>\r\n \t
      15. [latex]\\pi {a}^{2}b[\/latex]<\/li>\r\n \t
      16. [latex](\\frac{4}{3\\pi },\\frac{4}{3\\pi })[\/latex]<\/li>\r\n \t
      17. [latex](\\frac{1}{2},\\frac{2}{5})[\/latex]<\/li>\r\n \t
      18. [latex](0,\\frac{28}{9\\pi })[\/latex]<\/li>\r\n \t
      19. Center of mass: [latex](\\frac{a}{6},\\frac{4{a}^{2}}{5}),[\/latex] volume: [latex]\\frac{2\\pi {a}^{4}}{9}[\/latex]<\/li>\r\n \t
      20. Volume: [latex]2{\\pi }^{2}{a}^{2}(b+a)[\/latex]<\/li>\r\n<\/ol>","rendered":"

        Physical Applications<\/h2>\n
          \n
        1. [latex]150[\/latex] ft-lb<\/li>\n
        2. [latex]200\\text{J}[\/latex]<\/li>\n
        3. [latex]1[\/latex] J<\/li>\n
        4. [latex]\\frac{39}{2}[\/latex]<\/li>\n
        5. [latex]\\text{ln}(243)[\/latex]<\/li>\n
        6. [latex]\\frac{332\\pi }{15}[\/latex]<\/li>\n
        7. [latex]100\\pi[\/latex]<\/li>\n
        8. [latex]20\\pi \\sqrt{15}[\/latex]<\/li>\n
        9. [latex]6[\/latex] J<\/li>\n
        10. [latex]5[\/latex] cm<\/li>\n
        11. [latex]36[\/latex] J<\/li>\n
        12. [latex]18,750[\/latex] ft-lb<\/li>\n
        13. [latex]\\frac{32}{3}\u00d7{10}^{9}\\text{ft-lb}[\/latex]<\/li>\n
        14. [latex]8.65\u00d7{10}^{5}\\text{J}[\/latex]<\/li>\n
        15. \n
            \n
          1. [latex]3,000,000[\/latex] lb,<\/li>\n
          2. [latex]749,000[\/latex] lb<\/li>\n<\/ol>\n<\/li>\n
          3. [latex]23.25\\pi[\/latex] million ft-lb<\/li>\n
          4. [latex]\\frac{A\\rho {H}^{2}}{2}[\/latex]<\/li>\n
          5. Answers may vary<\/li>\n<\/ol>\n

            Moments and Centers of Mass<\/h2>\n
              \n
            1. [latex]\\frac{5}{4}[\/latex]<\/li>\n
            2. [latex](\\frac{2}{3},\\frac{2}{3})[\/latex]<\/li>\n
            3. [latex](\\frac{7}{4},\\frac{3}{2})[\/latex]<\/li>\n
            4. [latex]\\frac{3L}{4}[\/latex]<\/li>\n
            5. [latex]\\frac{\\pi }{2}[\/latex]<\/li>\n
            6. [latex]\\frac{{e}^{2}+1}{{e}^{2}-1}[\/latex]<\/li>\n
            7. [latex]\\frac{{\\pi }^{2}-4}{\\pi }[\/latex]<\/li>\n
            8. [latex]\\frac{1}{4}(1+{e}^{2})[\/latex]<\/li>\n
            9. [latex](\\frac{a}{3},\\frac{b}{3})[\/latex]<\/li>\n
            10. [latex](0,\\frac{\\pi }{8})[\/latex]<\/li>\n
            11. [latex](0,3)[\/latex]<\/li>\n
            12. [latex](0,\\frac{4}{\\pi })[\/latex]<\/li>\n
            13. [latex](\\frac{5}{8},\\frac{1}{3})[\/latex]<\/li>\n
            14. [latex]\\frac{m\\pi }{3}[\/latex]<\/li>\n
            15. [latex]\\pi {a}^{2}b[\/latex]<\/li>\n
            16. [latex](\\frac{4}{3\\pi },\\frac{4}{3\\pi })[\/latex]<\/li>\n
            17. [latex](\\frac{1}{2},\\frac{2}{5})[\/latex]<\/li>\n
            18. [latex](0,\\frac{28}{9\\pi })[\/latex]<\/li>\n
            19. Center of mass: [latex](\\frac{a}{6},\\frac{4{a}^{2}}{5}),[\/latex] volume: [latex]\\frac{2\\pi {a}^{4}}{9}[\/latex]<\/li>\n
            20. Volume: [latex]2{\\pi }^{2}{a}^{2}(b+a)[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":108,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/159"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/159\/revisions"}],"predecessor-version":[{"id":172,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/159\/revisions\/172"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/108"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/159\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=159"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=159"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=159"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}