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Câu hỏi: Cho hàm số $y=\cos 4x$ có một nguyên hàm $F\left( x \right)$. Khẳng định nào sau đây đúng?
A. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=1$
B. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=\dfrac{1}{4}$
C. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=-1$
D. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=\dfrac{-1}{4}$
A. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=1$
B. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=\dfrac{1}{4}$
C. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=-1$
D. $F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=\dfrac{-1}{4}$
Ta có: $F\left( x \right)=\int{\cos 4xdx}=\dfrac{1}{4}\sin 4x+C\Rightarrow F\left( \dfrac{\pi }{8} \right)-F\left( 0 \right)=\dfrac{1}{4}\sin 4\dfrac{\pi }{8}-\dfrac{1}{4}\sin 0=\dfrac{1}{4}$.
Đáp án B.