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Câu hỏi: Tổng diện tích $S={{S}_{1}}+{{S}_{2}}+{{S}_{3}}$ trong hình vẽ được tính bằng tích phân nào sau đây?
A. $S=\int\limits_{a}^{b}{f\left( x \right)dx}$
B. $S=\int\limits_{a}^{c}{f\left( x \right)dx}-\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$
C. $S=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{d}{f\left( x \right)dx}-\int\limits_{d}^{b}{f\left( x \right)dx}$
D. $S=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$
A. $S=\int\limits_{a}^{b}{f\left( x \right)dx}$
B. $S=\int\limits_{a}^{c}{f\left( x \right)dx}-\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$
C. $S=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{d}{f\left( x \right)dx}-\int\limits_{d}^{b}{f\left( x \right)dx}$
D. $S=\int\limits_{a}^{c}{f\left( x \right)dx}+\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$
$S={{S}_{1}}+{{S}_{2}}+{{S}_{3}}=\int\limits_{a}^{b}{\left| f\left( x \right) \right|dx}+\int\limits_{c}^{d}{\left| f\left( x \right) \right|dx}+\int\limits_{d}^{b}{\left| f\left( x \right) \right|dx}$.
$\Rightarrow S=\int\limits_{a}^{c}{f\left( x \right)dx}-\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$.
$\Rightarrow S=\int\limits_{a}^{c}{f\left( x \right)dx}-\int\limits_{c}^{d}{f\left( x \right)dx}+\int\limits_{d}^{b}{f\left( x \right)dx}$.
Đáp án B.