21f08-61 - Å º½º Ö × ÙÔ ØÓ x = b¸ ÓÛ Ø ÙÖÚ...

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Unformatted text preview: Å º½º Ö × ÙÔ ØÓ x = b¸ ÓÛ Ø ÙÖÚ × × Ø ØÓØ Ð Ö ¸ Ø ÌÀ ¾½¸ Äĸ ¾¼¼ ØÛ Ò ÙÖÚ ×º Ì Ö ØÛ Ò ÙÖÚ × y = f (x) Ò y = g(x)¸ ÓÖ¸ × Ý x = a × ÓÙÒ Ò Ø ÓÐÐÓÛ Ò ÔÖÓ ×× Ö Ø ÓÑ Ò [a, b] ÒØÓ ÙÒ Ó ×Ù ÒØ ÖÚ Ð׸ ∆xº ÇÚ Ö Ð ØØÐ Ô ¸ × Ý ÒØ Ö Ø Ø ÔÓ ÒØ xi ¸ Ø ×Ð Ú Ö Ó Ö ØÛ Ò Ø Ò ÐÑÓ×Ø Ö Ø Ò ÙÐ Ö Ö ÓÒ¸ Ó Ö ∆Ai = (g(xi ) − f (xi ))∆x¸ ÔÔÖÓÜ Ñ Ø Ðݺ Ì Ò¸ × n n i=1 (f (xi ) − g(xi ))∆x = Ø Ð ×Ø ÔÔÖÓÜ Ñ Ø Ðݺ Ç ÓÙÖ× ¸ × Ø Û Ø ∆x Ó Ø Ø ØÖÙ Ö ÑÔÖÓÚ ×¸ ×Ó Ø Ø Ø Ü Ø Ö A × ∆Ai, i=1 ×Ð × Ø× ×Ñ ÐÐ Ö¸ Ø ÔÔÖÓÜ Ñ Ø ÓÒ ØÓ n A = lim n→∞ i=1 (f (xi ) − g(xi ))∆x, Û × ab (f (x) − g(x))dxº ÒØ Ö × Ò ÐÓ× Ý ´½µ ´¾µ ´¿µ ´µ Ø Ø Ø Ø ÙÖÚ ÙÖÚ ÙÖÚ ÙÖÚ × × × × y y y y = x2 Ò y = 2x + 1º = x Ò y = x3 ´Ø × ÓÒ × Ø Ó Ø µº =√ arctan x Ò y = 4x/π Ì ÓÒ×Ø ÒØ× Ö ×ÙÔÔÓ× = 4 − x2 ¸ y = x¸ Ò y = −xº ØÓ ÐÔº ÆÓØ Ø Ø Ö Ø ÒØ Ö Ð × Ò Ü Ø Ú ÐÙ ÓÖ Ø Ö ¸ Û × ÔÔÖÓÜ Ñ Ø Ý Ø ×ÙÑ× Ð Ò ÙÔ ØÓ Ø ÒØ Ö Ðº Ì Ø³× Ø ÒÖÐ Û Ø ÔÔÐ Ø ÓÒ× Ó ÒØ Ö Ø ÓÒ ÝÓÙ ÔÔÖÓÜ Ñ Ø × ØÙ Ø ÓÒ Û Ø ÓÑ ØÖ ÐÐÝ Ö ×ÓÒ Ð ÑÓ Ð׸ Ò × Ø ÔÔÖÓÜ Ñ Ø ÓÒ Ø× Ò Ö Ò Ò Ö¸ ØÛÓ Ø Ò × ÔÔ Ò ´½µ Ì ´¾µ Ì ¹Ñ Ð ÔÔÖÓÜ Ñ Ø ÓÒ× ÔÔÖÓ Ø Ö Ð Ó Ø ØÓ Ñ ×ÙÖ ¸ Ò ÓÖÑÙÐ ÓÑ × Ø ÒØ Ö Ð¸ Ø Ð Ñ Ø Ó Ê Ñ ÒÒ ×ÙÑ׸ Ó ×ÓÑ ÙÒ Ø ÓÒº Ö ×× Ú º Ó Ò×ÓÒÐ º Ù ½ ...
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This note was uploaded on 11/24/2011 for the course MATH 21 taught by Professor Stanley during the Fall '09 term at Lehigh University .

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