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Câu hỏi: Tìm nguyên hàm $F\left( x \right)=\int{\left( x+\sin x \right)\text{d}x}$ biết $F\left( 0 \right)=19$.
A. $F\left( x \right)={{x}^{2}}+\cos x+20$.
B. $F\left( x \right)={{x}^{2}}-\cos x+20$.
C. $F\left( x \right)=\dfrac{1}{2}{{x}^{2}}-\cos x+20$.
D. $F\left( x \right)=\dfrac{1}{2}{{x}^{2}}+\cos x+20$.
A. $F\left( x \right)={{x}^{2}}+\cos x+20$.
B. $F\left( x \right)={{x}^{2}}-\cos x+20$.
C. $F\left( x \right)=\dfrac{1}{2}{{x}^{2}}-\cos x+20$.
D. $F\left( x \right)=\dfrac{1}{2}{{x}^{2}}+\cos x+20$.
Ta có: $F\left( x \right)=\int{\left( x+\sin x \right)\text{d}x}$ $=\dfrac{{{x}^{2}}}{2}-\cos x+C$
Mà $F\left( 0 \right)=19\Leftrightarrow -1+C=19$ $\Leftrightarrow C=20$
Vậy $F\left( x \right)=\dfrac{{{x}^{2}}}{2}-\cos x+20$.
Mà $F\left( 0 \right)=19\Leftrightarrow -1+C=19$ $\Leftrightarrow C=20$
Vậy $F\left( x \right)=\dfrac{{{x}^{2}}}{2}-\cos x+20$.
Đáp án C.