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Câu hỏi: Cho hàm số $y=f\left( x \right)$ và hàm số bậc ba $y=g\left( x \right)$ có đồ thị như hình vẽ bên. Diện tích phần gạch chéo được tính bởi công thức nào sau đây?
A. $S=\int\limits_{-3}^{-1}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}$
B. $S\left| \int\limits_{-3}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}} \right|$
C. $S=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}$
D. $S=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}$
A. $S=\int\limits_{-3}^{-1}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}$
B. $S\left| \int\limits_{-3}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}} \right|$
C. $S=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}$
D. $S=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}$
Ta có: $S=\int\limits_{-3}^{2}{\left| f\left( x \right)-g\left( x \right) \right|d\text{x}}=\int\limits_{-3}^{-1}{\left| f\left( x \right)-g\left( x \right) \right|d\text{x}}+\int\limits_{-1}^{2}{\left| f\left( x \right)-g\left( x \right) \right|d\text{x}}$
$=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}$.
$=\int\limits_{-3}^{-1}{\left[ g\left( x \right)-f\left( x \right) \right]d\text{x}}+\int\limits_{-1}^{2}{\left[ f\left( x \right)-g\left( x \right) \right]d\text{x}}$.
Đáp án C.