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Câu hỏi: Cho tích phân $\int\limits_{0}^{\dfrac{\pi }{2}}{\left( 4x-1+\cos x \right)dx}=\pi \left( \dfrac{\pi }{a}-\dfrac{1}{b} \right)+c,\left( a,b,c\in \mathbb{Q} \right)$. Tính $a-b+c$
A. $\dfrac{1}{2}$.
B. 1.
C. 2.
D. $\dfrac{1}{3}$.
A. $\dfrac{1}{2}$.
B. 1.
C. 2.
D. $\dfrac{1}{3}$.
Ta có $\int\limits_{0}^{\dfrac{\pi }{2}}{\left( 4x-1+\cos x \right)dx}=\left. \left( 2{{x}^{2}}-x+\sin x \right) \right|_{0}^{\dfrac{\pi }{2}}=\pi \left( \dfrac{\pi }{2}-\dfrac{1}{2} \right)+1$.
Suy ra a = 2, b = 2, c = 1 nên a – b + c =1.
Suy ra a = 2, b = 2, c = 1 nên a – b + c =1.
Đáp án B.