Cho hàm số f(x) có <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-1"><span class="MJXp-mstyle" id="MJXp-Span-2"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-3">f</span><span class="MJXp-mo" id="MJXp-Span-4" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mn" id="MJXp-Span-5">1</span><span class="MJXp-mo" id="MJXp-Span-6" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-7" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-8">2</span><span class="MJXp-mo" id="MJXp-Span-9" style="margin-left: 0.267em; margin-right: 0.267em;">−</span><span class="MJXp-mn" id="MJXp-Span-10">2</span><span class="MJXp-msqrt" id="MJXp-Span-11"><span class="MJXp-surd"><span style="font-size: 134%; margin-top: 0.104em;">√</span></span><span class="MJXp-root"><span class="MJXp-rule" style="border-top: 0.08em solid;"></span><span class="MJXp-box"><span class="MJXp-mn" id="MJXp-Span-12">2</span></span></span></span></span></span></span><span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML MJXc-processed" tabindex="0" style="font-size: 127%;"><span id="MJXc-Node-1" class="mjx-math"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mstyle"><span id="MJXc-Node-4" class="mjx-mrow" style="font-size: 120%;"><span id="MJXc-Node-5" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.495em; padding-bottom: 0.495em; padding-right: 0.06em;">f</span></span><span id="MJXc-Node-6" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">(</span></span><span id="MJXc-Node-7" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">1</span></span><span id="MJXc-Node-8" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.445em; padding-bottom: 0.593em;">)</span></span><span id="MJXc-Node-9" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.101em; padding-bottom: 0.298em;">=</span></span><span id="MJXc-Node-10" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span><span id="MJXc-Node-11" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.445em;">−</span></span><span id="MJXc-Node-12" class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span><span id="MJXc-Node-13" class="mjx-msqrt"><span class="mjx-box" style="padding-top: 0.045em;"><span class="mjx-surd"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.495em; padding-bottom: 0.544em;">√</span></span><span class="mjx-box" style="padding-top: 0.13em; border-top: 1.8px solid;"><span id="MJXc-Node-14" class="mjx-mrow"><span id="MJXc-Node-15" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.396em; padding-bottom: 0.347em;">2</span></span></span></span></span></span></span></span></span></span></span><script type="math/tex" id="MathJax-Element-1">\large f(1) = 2-2\sqrt{2} </script> và $\large f'(x) = \df

Cho hàm số f(x) có f(1)=222f(1)=222 và $\large f'(x) = \df

4.4/5

Tác giả: Thầy Tùng

Đăng ngày: 18 Aug 2022

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Câu hỏi:

Cho hàm số f(x) có f(1)=222f(1)=222 và f(x)=1(x+1)x+xx+1 với x>0. Khi đó: 31f(x)dx bằng 

Đáp án án đúng là: A

Lời giải chi tiết:

Chọn A

1(x+1)x+xx+1dx=(x+1)xxx+1(x+1)2xx2(x+1)dx

=(x+1)xxx+1x(x+1)dx=(1x1x+1)dx=2x2x+1+C

Suy ra: f(x)=2x2x+1+C

Mà f(1)=222C=0

Ta có: 

31f(x)dx=31(2x2x+1)dx=(43xx43(x+1)x+1)|31=4(3+2233)