X−a)cos3xb+1csin3x+2017 Thì Tổng S=a+b+c Bằng - Cungthi.online

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Câu hỏi

Một nguyên hàm ∫(x−2)sin3xdx=−(x−a)cos3xb+1csin3x+2017 thì tổng S=a+b+c bằng A.S =3 B.S =15 C.S =10 D.S =14 Đáp án và lời giải Đáp án:D Lời giải:Lời giải Chọn D Đặt: u=x−2dv=sin3x dx ⇒du=dxv=−13cos3x Do đó ∫x−2sin3xdx=−13x−2cos3x+13∫cos3x dx=−13x−2cos3x+19sin3x+C Theo bài ra thì ∫x−2sin3xdx=−x−acos3xb+1csin3x+2017 Do đó ta suy ra: a=2,b=3,c=9 . Suy ra : S=a+b+c=14 .

Vậy đáp án đúng là D.

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