21f08-52-53

# 21f08-52-53 - AFA8 5 h eÒ Øeg Öa Ð Ù Ðe × ÖÓÔÓ...

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Unformatted text preview: AFA8 5 h eÒ Øeg Öa Ð Ù Ðe × ÖÓÔÓ × iØ iÓÒ Ù Ðe× integraltext b a cdx = c ( b- a ) integraltext b a f ( x ) dx =- integraltext a b f ( x ) dx A ØÙa ÐÐÝ Øh i×ÖÙ Ðe i×adeÒ iØiÓÒehadÒ ØhadadeÒ iØiÓÒ fÓ Ö ØheÖ igh ØhaÒd× ide a ØÐea × ØÛ heÒ a < b ;Øh i×he ÐÔ × fÓ Ö×ÓÑ e Ða ØeÖ fÓ ÖÑ Ù Ða × integraltext a a f ( x ) dx = 0 A ×be fÓ ÖeØh i× i×Öea ÐÐÝadeÒ iØiÓÒ 4 integraltext b a cf ( x ) dx = c integraltext b a f ( x ) dx 5 integraltext b a f ( x ) ± g ( x ) dx = integraltext b a f ( x ) dx ± integraltext b a g ( x ) dx 6 f f ( x ) ≥ fÓ Öa ÐÐ x ∈ [ a,b ] a < b ØheÒ integraltext b a f ( x ) dx ≥ . 7 f f ( x ) ≥ g ( x ) fÓ Öa ÐÐ x ∈ [ a,b ] a < b ØheÒ integraltext b a f ( x ) dx ≥ integraltext b a g ( x ) dx. 8 F Ó Öa ÐÐ a b aÒd c integraltext c a f ( x ) dx + integraltext b c f ( x ) dx = integraltext b a f ( x ) dx. 9 f m ≤ f ( x ) ≤ M fÓ Öa ÐÐ x ∈ [ a,b ] a < b ØheÒ m ( b- a ) ≤ integraltext b a f ( x ) dx ≤ M ( b- a ) . vextendsingle vextendsingle vextendsingle integraltext b a f ( x ) dx vextendsingle vextendsingle vextendsingle ≤ integraltext b a | f ( x ) | dx h eÓ ÖeÑ f f i×ÓÒ ØiÒÙÓÙ ×ÓÒ [ a,b ] Ó Ö if f i×Ñ ÓÒÓ ØÓÒ eÓÒ [ a,b ] ØheÒ integraltext b a f ( x ) dx eÜ i× Ø× E ÜaÑ Ô Ðe F iÒd integraltext 3 − 2 | x | dx hÓÛ Øha Ø integraltext π/ 4 sin 3 xdx ≤ integraltext π/ 4 sin 2 xdx hÓÛ Øha Ø integraltext π sin 2 xdx = π/ 2 h e×aÑ e i×ØÖÙ e fÓ Ö cos 2 x integraltext π cos 2 xdx = π/ 2 5 h eF ÙÒd aÑ eÒ Øa Ðh eÓ ÖeÑ Ó fC a ÐÙ ÐÙ × F Ó Öa fÙÒ Ø iÓÒ f d eÒ edÓÒ [ a,b ] d eÒ e g ( x ) ØÓ b eØh ed eÒ iØe iÒ Øeg Öa ÐÓ f f fÖÓÑ a ØÓ x ÓÒÓÛ Øh eÙÔÔ e ÖÐiÑ iØÓ fiÒ Øeg Öa Ø iÓÒØh eÙÔÔ e ÖÚa ÐÙ e Ó fØh eÚa Ö iab ÐeØha ØfÓ ÖÑ ×Øh eeÒdÓ fØh eÖeg iÓÒb eÓÑ e×Øh e Úa Ö iab Ðe fÓ Öa fÙÒ Ø iÓÒ Ó ØehÓÛk eÔ ØaÛ aÝ fÖÓÑ ÒaÑ iÒg Øh eÚa Ö iab ÐeÓ f f ha Ø×b eaÙ ×eÓ fÓÙ ÖÖeÔ ea ØedÙ ×eÓ f x a × Øh eÚa Ö iab Ðea ÐÐØh eØ iÑ eÓÛÛ eaÒ ØÛ Ö iØe g ( x ) := integraldisplay x a f ( x ) dx, eÚ eÒ ØhÓÙgh Øha Ø×Û ha ØÛ eÖeØh iÒk iÒgb eaÙ ×eeah Ðe ØØe Ö i××ÙÔÔÓ ×ed ØÓÓÒ ÐÝ ×ØaÒd fÓ ÖÓÒ...
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21f08-52-53 - AFA8 5 h eÒ Øeg Öa Ð Ù Ðe × ÖÓÔÓ...

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