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Câu hỏi: Nếu $\int\limits_{{}}^{{}}{f\left( x \right)dx}=\dfrac{{{x}^{3}}}{3}+{{e}^{x}}+C$ thì $f\left( x \right)$ bằng
A. $f\left( x \right)=3{{x}^{2}}+{{e}^{x}}$
B. $f\left( x \right)=\dfrac{{{x}^{4}}}{12}+{{e}^{x}}$
C. $f\left( x \right)={{x}^{2}}+{{e}^{x}}$
D. $f\left( x \right)=\dfrac{{{x}^{2}}}{3}+{{e}^{x}}$
A. $f\left( x \right)=3{{x}^{2}}+{{e}^{x}}$
B. $f\left( x \right)=\dfrac{{{x}^{4}}}{12}+{{e}^{x}}$
C. $f\left( x \right)={{x}^{2}}+{{e}^{x}}$
D. $f\left( x \right)=\dfrac{{{x}^{2}}}{3}+{{e}^{x}}$
Phương pháp:
Sử dụng: $\int\limits_{{}}^{{}}{f\left( x \right)dx}=F\left( x \right)+C\Rightarrow f\left( x \right)=F'\left( x \right).$
Cách giải:
$\int\limits_{{}}^{{}}{f\left( x \right)dx}=\dfrac{{{x}^{3}}}{3}+{{e}^{x}}+C\Rightarrow f\left( x \right)=\left( \dfrac{{{x}^{3}}}{3}+{{e}^{x}}+C \right)'={{x}^{2}}+{{e}^{x}}.$
Sử dụng: $\int\limits_{{}}^{{}}{f\left( x \right)dx}=F\left( x \right)+C\Rightarrow f\left( x \right)=F'\left( x \right).$
Cách giải:
$\int\limits_{{}}^{{}}{f\left( x \right)dx}=\dfrac{{{x}^{3}}}{3}+{{e}^{x}}+C\Rightarrow f\left( x \right)=\left( \dfrac{{{x}^{3}}}{3}+{{e}^{x}}+C \right)'={{x}^{2}}+{{e}^{x}}.$
Đáp án C.