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Câu hỏi: Cho hàm số $f\left( x \right)={{\left( \sin x-\cos x \right)}^{2}}$. Khẳng định nào dưới đây đúng?
A. $\int{f\left( x \right)dx}=-x-\dfrac{1}{2}\cos 2x+C.$
B. $\int{f\left( x \right)dx}=-x+\dfrac{1}{2}\cos 2x+C.$
C. $\int{f\left( x \right)dx}=x-\dfrac{1}{2}\cos 2x+C.$
D. $\int{f\left( x \right)dx}=x+\dfrac{1}{2}\cos 2x+C.$
A. $\int{f\left( x \right)dx}=-x-\dfrac{1}{2}\cos 2x+C.$
B. $\int{f\left( x \right)dx}=-x+\dfrac{1}{2}\cos 2x+C.$
C. $\int{f\left( x \right)dx}=x-\dfrac{1}{2}\cos 2x+C.$
D. $\int{f\left( x \right)dx}=x+\dfrac{1}{2}\cos 2x+C.$
Ta có $f\left( x \right)={{\left( \sin x-\cos x \right)}^{2}}=1-2\sin x\cos x=1-\sin 2x$
Suy ra $\int{f\left( x \right)dx}=\int{\left( 1-\sin 2x \right)dx=} x+\dfrac{1}{2}\cos 2x+C.$
Suy ra $\int{f\left( x \right)dx}=\int{\left( 1-\sin 2x \right)dx=} x+\dfrac{1}{2}\cos 2x+C.$
Đáp án D.
