Cho hai hàm số \(y = {f_1}\left( x \right)\) và \(...
Câu hỏi: Cho hai hàm số \(y = {f_1}\left( x \right)\) và \(y=f_2 (x)\) liên tục trên đoạn [a;b] và có đồ thị như hình vẽ bên. Gọi S là hình phẳng giới hạn bởi hai đồ thị trên và các đường thẳng \(x=a, x=b\). Thể tích V của vật thể tròn xoay tạo thành khi quay S quanh trục Ox được tính bởi công thức nào sau đây?![](data:image/png;base64,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)
A. \(V = \pi \int\limits_a^b {\left[ {{f_1}\left( x \right) - {f_2}\left( x \right)} \right]dx} \)
B. \(V = \pi \int\limits_a^b {\left[ {f_1^2\left( x \right) - f_2^2\left( x \right)} \right]dx} \)
C. \(V = \int\limits_a^b {\left[ {f_1^2\left( x \right) - f_2^2\left( x \right)} \right]dx} \)
D. \(V = \pi \int\limits_a^b {{{\left[ {{f_1}\left( x \right) - {f_2}\left( x \right)} \right]}^2}dx} \)
Câu hỏi trên thuộc đề trắc nghiệm
Đề tham khảo thi HK2 môn Toán lớp 12 năm học 2018 - 2019