Lectures27and28 - Ò Øeg Öa Ø iÓÒÓ fca Ða ÖF ie Ðd...

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Unformatted text preview: Ò Øeg Öa Ø iÓÒÓ fca Ða ÖF ie Ðd × eÒÓÛ ØÙ ÖÒÓÙ Öa ØØeÒ Ø iÓÒ ØÓ Øh eÕÙ e×Ø iÓÒÓ fhÓÛ iÒ Øeg Öa Ðca ÐcÙ ÐÙ ×Ñ igh Øb e geÒ eÖa ÐiÞed fÓ Ö fÙÒ c Ø iÓÒ ×Ó fÑ Ó ÖeØhaÒÓÒ eÚa Ö iab ÐeØÑ igh ØhaÚ eÓccÙ ÖÖed ØÓ ÝÓÙ Øha ØØh eÖe×hÓÙ Ðd ×Ù cha Øh iÒga ×Ôa ÖØ ia ÐiÒ Øeg Öa Ø iÓÒØÓgÓa ÐÓÒgÛ iØh Ôa ÖØ ia Ðd ieÖeÒ Ø ia Ø iÓÒh i× i× iÒd eed Øh eca ×eaÒd iÒ fac ØÛ edÓÒ ØeÚ eÒÒ eed aÒÝÒ eÛ ÒÓ Øa Ø iÓÒ ;Û ecaÒ × iÑ Ô ÐÝÛ Ö iØe ´ f ( x, y ) dx aÒd ´ f ( x, y ) dy h e d ieÖeÒ Ø ia Ðid eÒ Ø ie×Øh eÚa Ö iab ÐeÓ fiÒ Øeg Öa Ø iÓÒ fÓ ÖÙ ××Ó fÓ ÖØh e fÓ ÖÑ eÖÛ e ØÖea Ø y a ×acÓÒ ×ØaÒ ØaÒd fÓ ÖØh e Ða ØØeÖÛ eØÖea Ø x a ×acÓÒ ×ØaÒ Øh eÓÒ ÐÝ ØÛ i×Ø i×Øha ØÛ ha ØÛ eÖeÙ ×ed ØÓca ÐÐiÒg Øh ecÓÒ ×ØaÒ ØÓ fiÒ Øeg Öa Ø iÓÒÒ eedÓÒ ÐÝ b ecÓÒ ×ØaÒ Ø Û iØhÖe×Ôec ØØÓ ØheÚa Ö iab ÐeÓ fiÒ ØegÖa ØiÓÒ ;iØÑ aÝd eÔ eÒdÙÔÓÒ Øh e Ó Øh eÖÚa Ö iab Ðe × aÒdÙÒ Ðe××Û ekÒÓÛ Ó Øh eÖÛ i×eÛ eÑ Ù ×ØÛ Ö iØe iØa ××Ù ch E ÜaÑ Ô Ðe : ´ ( x 2 + y 2 ) dy = x 2 y + y 3 3 + g ( x ) . h i× i××ØÖa igh Ø fÓ ÖÛ a Öd eÒÓÙghbÙ Ø iØ i×Ò ØÖea ÐÐÝ iÒ Øeg Öa Ø iÓÒ ;iØ× jÙ ×ØaÒ Ø id ieÖeÒ Ø ia Ø iÓÒ Øh e×ea ÖeÒÓ ØØh e×aÑ eØh iÒg ;Øh eÝ jÙ ×ØhaÔÔ eÒ ØÓb eÖe Ða Øed ØÓ eachÓ Øh eÖiÒ × iÒg ÐeÚa Ö iab Ðeca ÐcÙ ÐÙ ×bÝ Øh eF ÙÒdaÑ eÒ Øa Ðh eÓ ÖeÑ Ó fC a Ð cÙ ÐÙ × fÛ eÛ aÒ ØØÓgeÒ eÖa ÐiÞeØh e cÓÒ ceÔ Ø Ó fiÒ Øeg Öa Ø iÓÒÛ ehaÚ eØÓgÓback ØÓ Øh eÓ Ö ig iÒa ÐÑ Ó Ø iÚa Ø iÒgÔ ÖÓb ÐeÑÛ h ichÛ a ×Øha ØÓ fÒd iÒgØh ea Öeab e ÐÓÛ a cÙ ÖÚ eh ecÓ ÖÖe×ÔÓÒd iÒgÔ ÖÓb ÐeÑ fÓ Öa fÙÒ c Ø iÓÒÓ f ØÛ Ó Úa Ö iab Ðe× i×Øh eÔ ÖÓb ÐeÑ Ó fÒd iÒgØh e ÚÓ ÐÙÑ ebe ÐÓÛ a×Ù Ö face aÒd ×Ó Øh i× i×Û h eÖeÛ e ÐÐ×Øa ÖØ ed Ðik eØÓ ÖeÔ ea ØÓÙ Ö×ØeÔ × fÖÓÑ a Øh7bÙ ØØh i×Ø iÑ eØh edÓÑ a iÒÓ f ÓÙ Ö fÙÒ c Ø iÓÒ f ( x, y ) i×a Öeg iÓÒ iÒ Øh e xy Ô ÐaÒ eF Ó ÖØh eØ iÑ eb e iÒgÛ e ÐÐa ××ÙÑ e Øh i×dÓÑ a iÒ ØÓb eÖec ØaÒgÙ Ða Ö : ( a, b ) × ( c, d ) Û e ÐÐÖe ØÙ ÖÒ ØÓÒÓÒ Öec ØaÒgÙ Ða Ö dÓÑ a iÒ ××ÓÓÒ aÒdÛ e ÐÐa ××ÙÑ eØha Ø f > eÚ eÖÝÛ h eÖe iÒ Øh i×dÓÑ a iÒ • F iÖ×ØÔa ÖØ iØ iÓÒ Øh e x aÜ i× iÒ ØÓ m iÒ ØeÖÚa Ð×Ó fÐeÒg Øh Δ x = ( b- a ) m aÒda Ð×Ó Ôa ÖØ iØ iÓÒ Øh e y aÜ i× iÒ ØÓ n iÒ ØeÖÚa Ð×Ó fÐeÒg Øh Δ y = ( d- c ) n h eeec Ø i×ØÓ Ôa ÖØ iØ iÓÒ Øh eeÒ Ø iÖedÓÑ a iÒ iÒ ØÓ Öec ØaÒg Ðe×Ó fd iÑ eÒ × iÓÒ × Δ x Δ y Øh e×e Öec ØaÒg Ðe×Øh eÒhaÚ ea Öea Δ A = Δ x Δ y • Ò eachÓ fØh e×eÖec ØaÒg Ðe×chÓÓ ×eaÔÓ...
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