Giải bài 39 trang 21 sách bài tập toán 12 - Cánh diều

Cho (intlimits_{ - 1}^2 {gleft( x right)dx} = 6,Gleft( x right)) là một nguyên hàm của hàm số (gleft( x right)) trên đoạn (left[ { - 1;2} right]) và (Gleft( { - 1} right) = 8). Tính (Gleft( 2 right)).

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Đề bài

Cho \(\int\limits_{ - 1}^2 {g\left( x \right)dx} = 6,G\left( x \right)\) là một nguyên hàm của hàm số \(g\left( x \right)\) trên đoạn \(\left[ { - 1;2} \right]\) và \(G\left( { - 1} \right) = 8\). Tính \(G\left( 2 \right)\).

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Lời giải chi tiết

Vì \(G\left( x \right)\) là một nguyên hàm của hàm số \(g\left( x \right)\) trên đoạn \(\left[ { - 1;2} \right]\) nên ta có: \(\int\limits_{ - 1}^2 {g\left( x \right)dx} = \left. {G\left( x \right)} \right|_{ - 1}^2 = G\left( 2 \right) - G\left( { - 1} \right)\). Khi đó ta có: \(6 = G\left( 2 \right) - 8\). Vậy \(G\left( 2 \right) = 14\).

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ꦕ Giải bài 40 trang 22 sách bài tập toán 12 - Cánh diều Cho (intlimits_{ - 2}^1 {fleft( x right)dx} = 5) và (intlimits_{ - 2}^1 {gleft( x right)dx} = - 4). Tính: a) (intlimits_1^{ - 2} {fleft( x right)dx} ); b) (intlimits_{ - 2}^1 { - 4fleft( x right)dx} ); c) (intlimits_{ - 2}^1 {frac{{ - 2gleft( x right)}}{3}dx} ); d) (intlimits_{ - 2}^1 {left[ {fleft( x right) + gleft( x right)} right]dx} ); e) (intlimits_{ - 2}^1 {left[ {fleft( x right) - gleft( x right)} right]dx} ); g) (intlimits_{ - 2}
𒁏 Giải bài 41 trang 22 sách bài tập toán 12 - Cánh diều Cho (intlimits_{ - 1}^3 {fleft( x right)dx} = 2,intlimits_2^3 {fleft( x right)dx} = - 5). Tính tích phân (intlimits_{ - 1}^2 {fleft( x right)dx} ).
♈ Giải bài 42 trang 22 sách bài tập toán 12 - Cánh diều Một ô tô đang chạy với vận tốc (18m/s) thì người lái ô tô đạp phanh, từ thời điểm đó, ô tô chuyển động chậm dần đều với vận tốc (vleft( t right) = - 6t + 18left( {m/s} right)), trong đó (t) là thời gian tính bằng giây. Hỏi từ lúc đạp phanh đến khi dừng hẳn, ô tô di chuyển được quãng đường bằng bao nhiêu mét?
🐟 Giải bài 43 trang 22 sách bài tập toán 12 - Cánh diều Một vật chuyển động với vận tốc được cho bởi đồ thị ở Hình 3. a) Tính quãng đường mà vật di chuyển được trong 5 giây đầu tiên. b) Tính quãng đường mà vật di chuyển được từ thời điểm 1 giây đến 5 giây.
ꦅ Giải bài 38 trang 21 sách bài tập toán 12 - Cánh diều Nêu một ví dụ chỉ ra rằng (intlimits_a^b {frac{{fleft( x right)}}{{gleft( x right)}}dx} ne frac{{intlimits_a^b {fleft( x right)dx} }}{{intlimits_a^b {gleft( x right)dx} }}) với (fleft( x right)) và (gleft( x right)) liên tục trên đoạn (left[ {a;b} right],gleft( x right) = 0,forall x in left[ {a;b} right]).

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