Calculus

Integration by part


  • 鹨ҡٵ ԿŤٳ
  • 鹶ǧ͡ 价ͧ
  • integrate Ш +, -
  • ǧ͡ Կ 价駤
  • ½ٵ Integration by part

ػ
  1. ٵѺͧ Integration by part
  2. ӤѺ climax ͧͧ õѴԹ͡ u, dv ФѺ
Integration by part [ԸѴ]
  1. [ѧѹ ع] x [ѧѹ ⡳] (x+2)(sin 2x)
  2. [ѧѹ ع] x [ѧѹ expo] (x^2)(e^2x)
  3. [ѧѹ expo] x [ѧѹ ⡳] (e^x)(cos x)

˵ õͧ 3 format ҹ鹶֧зẺԸѴ

鹵͹÷

  • [ѧѹ ع] x [ѧѹ ⡳ expo] (Ẻ 1, 2) ӵӴѺѧ
    1. ع , ⡳ expo
    2. Կ ҹ 0
    3. Թõ ҹ ÷ѴҡѺҹ
    4. ٳ§ŧ
    5. ͧѺѾ ٳ
    6. ӼŷҤԴ(ҵͧԴ) ͵ͺ(ͧԴ)
  • [ѧѹ expo] x [ѧѹ ⡳] (Ẻ 3)
    1. expo , ⡳
    2. ԹõҹҨ(ʹͧ)
    3. Կ ҹ ÷ѴѡѺҹ
    4. ٳ§ŧ
    5. ͧ
    6. ٳ÷Ѵش Integrate
    7. ͧ 6
    8. ӼŷҤԴ ǵͺ
  • Basic Limits


Example Ҥ
  • 鹵͹áͧ limit ᷹ͧ͡ x ҡѺ 2 ŧá͹ »ԡ
  • ù֡ ԤѺⴹ͡
  • ͧͧ¡͡ ҵѴ͢鹵͹
  • Ѵ͹ѹ駺ҧ
  • ᷹ͧ x ҡѺ 2 ŧա
  • ѧ䧤ѺҡѺ Щй鹤ͺ 㹵͹áⴹ



http://www.thaicalculus.com/main_template.php?id=14
http://www.thaicalculus.com/ex_template.php?id=1

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