Cho hàm số [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image168.png] biết [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image169.png] và [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image170.png] , biết $ \int _{ 0 }^{ \frac { \pi } { 2 } } { \frac { f\left ( { x } \right ) } { sin ^ { 2 } x+1 }dx=a-\frac { b\pi } { c } } $. Tổng $ S=a+b+c $ bằng

Question

Beedemy · Accepted Answer

Lời giải: Ta có [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image173.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image174.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image175.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image176.png] Vì [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image169.png] nên [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image177.png] . Vậy [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image178.png] Xét [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image179.png] . Cách 1: Đặt [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image180.png] ; Đổi cận: [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image181.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image182.png] . Xét [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image183.png] , đặt [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image184.png] . Đổi cận: [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image185.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image186.png] . Vậy [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image187.png] . Cách 2: Đặt [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image188.png] .Lấy vi phân 2 vế, ta có [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image189.png] ; Đổi cận: [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image190.png] [IMAGE:question_images/12-CD17. TICH PHAN/F. BAI TAP NANG CAO 3/image191.png] . Vậy $ S=a+b+c=6 $.

Bài tập nâng cao Tích phân · Bài 143