Tus Mean Value Theorem rau Integrals yog ib qho cuab yeej muaj zog, uas tuaj yeem siv los ua pov thawj Fundamental Theorem of Calculus Fundamental Theorem of Calculus Lub hauv paus theorem ntawm calculus yogtheorem uas txuas lub tswvyim ntawm kev sib txawv. muaj nuj nqi (xws li gradient) nrog lub tswv yim ntawm kev sib koom ua ke ib txoj haujlwm (xws li cheeb tsam hauv qab qhov nkhaus). … Qhov no txhais tau hais tias muaj cov tshuaj tiv thaiv rau kev ua haujlwm tas mus li. https://en.wikipedia.org › Fundamental_theorem_of_calculus
Fundamental theorem of calculus - Wikipedia
thiab kom tau txais tus nqi nruab nrab ntawm kev ua haujlwm ntawm ib ntus. Ntawm qhov tod tes, nws qhov hnyav version yog heev siv tau rau kev ntsuasqhov tsis sib xws rau qhov tseeb integrals.
Lub ntsiab lus Theorem rau Integrals txhais li cas?
Dab tsi yog Qhov Ntsuas Tus Nqi Theorem rau kev sib koom ua ke? Qhov ntsuas tus nqi nruab nrab rau kev sib xyaw qhia peb tias, rau kev ua haujlwm txuas ntxiv f (x) f (x) f (x),muaj tsawg kawg yog ib qho taw tes c hauv lub caij nyoog [a, b] uas tus nqi ntawm qhov muaj nuj nqi yuav sib npaug rau qhov nruab nrab tus nqi ntawm kev ua haujlwm dhau lub sijhawm ntawd.
Koj pom qhov txiaj ntsig ntawm qhov sib piv li cas?
Hauv lwm lo lus, lub ntsiab lus tus nqi theorem rau kev sib koom ua ke hais tias muaj tsawg kawg ib lub ntsiab lus c hauv lub sijhawm [a, b] qhov twg f(x) attains nws tus nqi nruab nrab ¯f: f (c)=¯f=1b−ab∫af(x)dx. Geometrically, qhov no txhais tau tiashais tias muaj ib daim duab plaub uas nws cheeb tsam raws nraim nruab nrab ntawm cheeb tsam nyob rau hauv lub nkhaus y=f(x).
Tus nqi txhais tau li cas theorems rau derivatives thiab Integrals ntsig txog?
Tus Mean Value Theorem rau Integrals yog a qhov txiaj ntsig ncaj qha ntawm Tus Mean Value Theorem (rau Derivatives) thiab Thawj Qhov Tseem Ceeb ntawm Calculus. Hauv cov lus, qhov txiaj ntsig no yog qhov ua haujlwm tas mus li ntawm qhov kaw, lub sijhawm ciam teb muaj tsawg kawg yog ib qho taw tes uas nws sib npaug rau nws qhov nruab nrab tus nqi ntawm lub sijhawm.
Koj ua li cas pom qhov txiaj ntsig ntawm C uas txaus siab rau Mean Value Theorem rau Integrals?
Yog li koj yuav tsum:
- nrhiav qhov tseem ceeb: ∫baf(x)dx, then.
- faib los ntawm b−a (qhov ntev ntawm lub sijhawm) thiab, kawg.
- set f(c) sib npaug rau tus lej pom hauv qib 2 thiab daws qhov sib npaug.
